http://forums.vwvortex.com/showthread.php?3344454
^This is the thread where I got my inspiration from. There are a couple differences as the thread pertains specifically to Corrados, but extremely similar for the most part. First conversion I did was on my own car, the '97 Jetta GLX swap. That was in early 2011 if I recall.
The front bracket that needs to be cut out of the Corrado is non-existant on the B4 Passat and Mk3 Jetta. So you don't have to worry about that step.
You do, however, need to cut away the left front portion of the opening in the chassis to clearance the lever mechanism.
I personally have been using the method in the above link where I install longer bolts in the front of the box and use spacers to keep it approximately level. I also elongate the holes on the back of the 02J shift box to line up with the square nuts welded to the rear mounting bracket for the shift box.
I use foam (sometimes carpet padding, I've also used other insulating foam a local kitchen and bathroom place in Maine literally gave to me for nothing) to fill in the gaps between the shift box and the body of the car. I like doing that as it usually ends up making the car even quieter than it was before. Plus the spacing means the shift lever isn't intruding as far into the chassis as before, the shift boot doesn't have to stretch and the lever is in a more normal position.
You can also use a Mk4 or newer shift knob on the car. I've done this with Brian's B4 Passat here as well as my own Mk3. My B4 has got a 6 speed knob out of a newer GTI. It seems to sit a fair bit lower on the lever than the standard 5 speed ones do, making the throws slightly shorter than with the Mk4 knob.
A number of these conversions I've also cut 12 x 1.50 mm threads in the top of the lever so you can use the original shift knob if so desired. It's a bit of a pain, though. And I'm pretty sure my Snap-on 12x1.50 die is a little worse for wear after doing a couple of these. Though, to be fair, that particular die got a lot of use in other repairs as well... Starting the threads on one of these levers is certainly not the easiest, though. The lever is a bit on the thick side for 12mm, but it's doable without shaving it down.
The biggest trick is sourcing shift towers, honestly. Many junkyards don't like removing an integral part of a transmission like that. Thank goodness for u-pull it style junkyards, though! They don't give a flying crap about what parts you take off their cars. Half the time they don't even know what it is I pull off the car when I show up with a shift tower. They'll fumble around in their computer system attempting to make up a name and price for it. As you can imagine, the prices I've paid for these parts are very inconsistent, even though I tend to source them from the same corporate junkyards (Pick-n-Pull in California).
Fortunately, early Mk4s are becoming a more common site in these style yards. Every time I go to one, I specifically am on the lookout for these shift linkages.
EDIT: Oh, also, I sometimes have to bend one of the intercooler pipe brackets upwards (the one behind the battery) a bit to ensure the shift weight doesn't hit the pipe when engaging 5th gear. That is a B4 Passat specific issue, though. The mk3 has the intercooler piping routed more towards the front of the car and away from the shift linkage.