1991
Philips
At first Philips and Nintendo are developing a SNES CD-Rom that is going to be compatible with Philips's CD-I machine. Nintendo would (as usual) have complete control over licensing the games for their SNES addon and Philips would supply them with the CD player. Philps also got the rights to use some of Nintendo's characters in some of their CD-I games. One Mario game was released (a puzzle game) and 3 rather crappy Zelda games. Nintendo were planning to introduce the machine on the C.E.S. in June, but unfortunately the deal that they had struck with Philips recently, inflicted with a previous deal (1988) with Sony, Philips's worst competitor...

Sony
Nintendo switched sides and instead the Playstation was introduced at the CES in June the same year! The machine was playing both special "Super Discs" containing 680 Megabyte but also normal SNES games. All was looking just fine until they found that the deal they had struck with Sony way back in 1988 granted Sony the right to control and license all the CD based games for the Playstation. Sony was also the only supplier of the special sound chip that was used in the SNES. Nintendo was in deep shit! (Or as one industry consultant put it "Sony had Nintendo by the balls..!"
 
Philips again...
Nintendo quickly announced that they had allied themselves with Philips once more, because "Philips's technology were superior". I especially like the comment one industry consultant made: "...It (Nintendo's cooperation with Philips) was meant to do two things: Give Nintendo back it's stranglehold on software and gracefully get one up on Sony!"!
 
Tumult at the C.E.S.
Sony tried to make Nintendo change their minds by threatening to sue them but Nintendo insisted on that their co-operation wouldn't interfere with Sony and Nintendo's CD project (the Playstation) so Sony waited to see. Sony shouldn't have trusted Nintendo this time because at the next C.E.S press conference about the Playstation, Nintendo stabbed them in the back.
The Sony people were expecting that Nintendo would be there and propagate for the Playstation but instead they announced their plans to work exclusively with Philips. Sony commented the incident by claiming that they had an exclusive deal with Nintendo that Nintendo had violated!

Negotiations...
In USA, this would lead to lawsuits no doubt but since both companies were Japanese things were taken care of in other manners/ways. First of all, there were a policy among Japanese companies not to turn against each other if it benefited foreign competitors. On the other hand Sony would win on solving their problems with Nintendo instead of exacerbating them, because of the Playstation's ability to play SNES games  (which Sony could profit from). Nintendo could also benefit from their relationship if they won better terms (like the control over the CD games). If they didn't 'make up' with Sony as soon as possible, Nintendo would sure get problems getting more of their precious SNES sound chips...
Because of the ambiguity and "vagueity"  of the Japanese contracts, Nintendo managed to extricate itself from the bad parts of the contract with ease and Nintendo continued to work with Philips...

Tokyo International Electronics Show
When it was clear to Sony that they wouldn't get any help from Nintendo with new CD games for the Playstation, Sony decided that it was time to show the world that they could manage on their own.

On the Tokyo International Electronics Show in October they put on a big show previewing the console, which they presented as a console both for gaming and education. A whole bunch of various educational multimedia titles were announced, amoung them: Compton's Enemy Encyclopedia, Software Toolworks world atlas, Microsoft bookshel 1991 edition, languages of the world, National Geographic Mammals of the world and a title called Mixed up Mother Goose. No real games were presented, though. But Sony were signing deals with other game developers. And still the Playstation would be able to run all old SNES games (just like Philips and Nintendo's machine). The release schedule is set 6 month before Philips and Nintendo's machine.
 

 
Playstation tech specs, from Electronic Gaming Monthly dated around October 1991:

Sustained data rate 150 Kbyte/sec   Memory buffer 64Kbit Burst data rate 600 Kbyte/sec   CD-I compatible Yes Average access time 0,34 sec   Price: (in USA) $200 Full stroke access time 0,53 sec   Released date (USA) January 1993

 
1992
On the January CES show Nintendo made an official announcement that they were abandoning their partnership with Sony.
Philips is working together with Nintendo and they announced that the release date would be by Christmas that same year. Later they changed the release date to 1993 and at he CES, Nintendo announced that they would use the same licensing system as they had used with their NES and SNES.

Here follows a list of tech specs from Electronic Gaming Monthly dated around June-July 1992:

 
Sega and Sony joins forces!
Mega CD was released for $300. Sony helped Sega instead by making games for their CD system!

Sony and Nintendo began negotiating again...
The companies grew tired of all the different CD formats on the market and in an attempt to create a industry wide standard executives from the largest Nintendo licensees met with Hiroshi Yamauchi to persuade him to join forces with Sony again. This way Both Nintendo, Philips and Sony would be using the same CD standard and that would be the worldwide one.
At last Nintendo began negotiate with Sony again (while they were still co-operating with Philips). Their negotiations with Sony finally resulted in a agreement between the two companies in October 1992: In the deal Nintendo got the rights to control and license all games for both Sony's Playstation and Nintendo's own machine and Sony controlled all non-game software's. Nintendo even controlled Sony's own games for the format!
This is Sony' comment about the deal: "We concluded that we had to ally ourselves with Nintendo when we saw that it was going to be the 16-bit winner. We wanted access to all those Nintendo players". It was also decided that the machine would be 32-bit instead of 16-bit (Sega's CD add-on was just 16 bit).

Sony, Nintendo and Philips
After the reunion with Sony, Nintendo starts developing a new console, the SNES Nintendo Disk a.k.a. Philips CD-ROM XA. This time Nintendo cooperated with both Sony AND Philips to make this new console. Some sources says that Nintendo only had a slight interest in developing this new CD system (because they stood to profit more from a cart based model and that other CD systems like the SEGA CD and NEC's cd were faltering.

Last known Tec specs...

The Games!
There wasn't many games announced for the ND...
The adventure game 7th Guest ported from the PC by Virgin and a game called Gdleen from Seta was on the way though. Other titles that were planned were Robocop and Cosmic osmo. These both titles later ended up on the PC format instead. Also a new Final Fantasy game was rumoured to be released to the ND. A new Zelda, Mario and a Street Fighter sequel was also rumoured.

The ND-disks cartridges- a package consisting of a CD and little memory chip for save games.

How the system worked...

A SNES cartridge named the System cartridge, was put in the normal cartridge slot. This cart contained a chip that handled the communication between the SNES and the NCD add-on's RAM memory using a system called H.A.N.D.S. which stands for Hyper Advanced Nintendo Data transfer System. The CD Rom drive, CPU and RAM etc was attached  beneath the SNES (see picture above.), through it's bottom expansion slot.

3. Outcome...

The sad ending and speculations about when and why Nintendo abandoned the project and what consequences that might had.

The sad ending...
In August 1992 Nintendo announces the advent of their new Super FX chip. This has the affect that Nintendo delays their CD add-on more. The CD-Rom had to be upgraded to be better than the S-FX chip!
In early 93 Nintendo announced some new tech specs about the machine: It's CDs would contain 540 Mbytes  and the games released for the format would probably be compatible with one of Philips's machines, probably the CD-I... The machine was also made known as the Philips CD-ROM/XA.The we also rumours about a new Zelda game and a Street Fighter 2 sequel for the SNES CD. The release date was set to Autumn 1993 but the price was still $200. Nintendo promises to show the CD addon on the S.C.E.S show later the same year...

S.C.E.S. Chicago -93
Nintendo had promised to reveal their ND on the S.C.E.S in Chicago 93 and they had also said that it would be released in early 1994. When the S.C.E.S. came Nintendo didn't showed any CD system at all instead they introduced new S-FX games like FX-Trax (a.k.a. Stunt Race FX) and Super Mario Allstars but not a word about any CD. Later that year Nintendo announced that they wouldn't release any SNES CD at all.

Outcome
The main effect of Nintendo's abandoning of their CD project with Sony and Philip was that the machine that Sony and Nintendo were planning on first, the Playstation was later released by Sony as the standalone console that today is the worst competitor of the Nintendo 64.
Note: None of the original chipset or technology from the Nintendo/Sony SNES add-on was used in the Playstation that we know today. The new 32-bit console was re-designed from scratch.
 
To sort things out there were 3 different Nintendo CD consoles:
1. The Playstation which Nintendo and Sony were planning on based on the their deal with Nintendo from 1991.
2. The Nintendo/Philips CD-ROM add-on based on the agreement between Philips and Nintendo around the time of the C.E.S. in June 1991.
3. The Philips CD-ROM XA / SNES Nintendo Disk which were a product of the cooperation between both Nintendo, Sony and Philips. Based on a deal struck around October - November 1992.

Why did Nintendo abandon the CD system...?
Still we haven't found out what made Nintendo so quickly change their minds from thinking that the CD-Rom was the future of video gaming to that it sucked! They said that it was to limited because of it's long loading times and the fact that it was an read-only medium. Nintendo then began to work on the Nintendo 64 and the Virtual Boy instead.
Other factors may be that Nintendo figured that they would make more profits with the cartridge based system than the CD system and the fact that the CD was very easy to copy. Nintendo may also has judged that a cartridge based console would be better in fear that their new console would die out like Sega and NEC's cd systems...

Was it the right thing to do?
I think that abandoning the SNES ND was Nintendo's biggest mistake ever because if they had released their CD add-on, the Playstation and the Saturn wouldn't have such a big advantage as they have today because of the huge delays of the N64 that occurred. If Nintendo had released their CD system before the Playstation and Saturn was released, I think people would prefer Nintendo's CD rather than Sony and Philip's machines.
Also if Nintendo had continued working with Sony, the Playstation wouldn't have competed with Nintendo's own CD in the same way since the both CD systems would have used the same CD format etc, and maybe the Saturn had never ever been produced! From this point of view you can say that Nintendo dug their own grave when they abandoned Sony's Project.
 
Just for the fairness of thing I'll end this article with a quote from Nintendo's own Nintendo Power article, "Nintendo Power" publication, "The next time when someone tells you that CD-ROM is the wave of the future, tell them that the future doesn't belong to the snails"