Hi there chap.
This is advice passed from one amateur to another

, but essentially; the clip around the long black tube/hose connecting the throttle body has 2 prongs sticking out. If you use a pair of pliers to squeeze them together, it loosens the clip, and you can work the clip back down the pipe, and work the pipe off the throttle body.
Then the throttle body will be held on by 4 x 10mm or 13mm bolts. Can be a little awkward to get the bottom 2 off, but not too hard. Once they're off (and the connected pipes), you can remove the throttle body from the engine.
To clean it, you'll need a can (spray can) of carb cleaner from halfrauds/motorfactors, a toothbrush, and a rag.
Put the throttle body in a bowl of some sort, and apply carb cleaner liberally (internally). Spray some carb cleaner onto a rag, and use it to thoroughly clean the inside of the throttle body. Tis a big tube. You can get 3 fingers in there. Can't go wrong. You'll see the dirt coming off..
There will be a lever of sorts on the side of the throttle body that opens and closes a plate inside the throttle body (which controls airflow, you'll know it when you see it

, big old butterfly valve of sorts). You'll want to find a way of holding that open while you're cleaning, so that you can clean through the whole throttle body...
Once you're done with the rag, clearing out as much oil/grime as you can, go at it again with the toothbrush. Using plenty of carb cleaner. Paying close attention to the slot/gap that the plate opens from/closes into (this is the area that causes the rough idle/cutting out. The valve doesn't close fully, because grime blocks it, allowing air to flow though).
The main issue with them tends to relate to them getting a little gunked up. The butterfly valve thing doesn't close fully, due to gunk.. Air passes through, and you wind up with a rough idle^. Definately worth a go. it's solved 3 rough VW idles in a row for me..
After putting everything back together, you would ideally use VAG COM to re-align the throttle body (re-sync the actual position of the butterfly valve that you just cleaned out with the position perceived by the ECU). Though I do believe that by leaving the battery disconnected for 30 mins and then driving 40+ miles the ECU will adapt, and perform the same function, essentially, without having to run VAG COM. But don't quote me..
VAG COM is a piece of software used to read VAG (Volkswagen Audi Group.. And a bunch of other names I cba to go into) sensor codes, and reset/play around with pre-programmed maintenance procedures.
You would install it onto a laptop, then use a USB>OBD-II cable to plug yourself into the car's OBD port, and fire up VAG COM to access all of the fun bits.
In truth though, it costs a small fortune, and is a pita to install and deal with, for the sake of a simple code reading. If you're not that way inclined, and don't intend to use it regularly, it's not overly easy to navigate/install/deal with, and not cost effective.
If your current mechanic doesn't have a copy, he's most likely the wrong chap for the job (Kwik Fit are never, ever the right chaps for the job..)..
Best bet is to phone around locally and find an indy that can read/reset VW codes of the era. Clean the throttle body yourself; and then take it to them to have the codes read, throttle body re-alligned (using the software), and the codes reset. It shouldn't cost you more than £30. Then go back to Kwik Fit.
Though tbh chap (I'd feel bad for if I were to not say this..), Kwik Fit are the last people you should be taking your car to. They're rather unreliable.
Edit: Watch a bunch of youtube 'VW throttle body cleaning' guides, to get an idea of what you're up against. It's very simple stuff so long as you can get the thing off in the first place. No more difficult than cleaning a PC case or something similar. Have a look at a few vids to get yourself acquainted.