Here is the single most powerful routine to do that. It targets specifically co-ordination, so you must make sure that the technique required for the passage had been thoroughly mastered by previous work on hands separate.

I call it “dropping notes”.

The student should start by playing the right hand (for example – it doesn’t really matter which hand you start). He plays the right hand only a couple of times. If it is fluent and smooth, the student is now going to add the first, and only the first note of the left hand. In other words, s/he is going to “drop” the first LH note. The aim is to keep the RH going no matter what. It does not matter if the LH note is wrong: it can be fixed later. The only thing that matters is that the RH should continue undisturbed, no matter what the RH is doing. It is going to take 2 or 3 (maybe more) repeats for the student to get the hang of it. Once s/he can do it, add the next note. To start with everything will fall apart. Never mind, keep trying. First aim to keep the RH going no matter what. Once this is accomplished, to get the LH notes right. It is all a matter of priorities. At this stage the priority is not to get the LH notes perfect at the expense of the RH movement. All we are interested in, is to get the RH to move independently of what the LH is doing. Once we accomplish this, them we can turn our attention to accuracy.

Keep adding the LH notes one by one. Every time you add a new note, everything falls apart, but as you proceed, it gets easier and easier. Eventually you will be playing hands together!

Now comes a very important step that must not be skipped. You must do it all over again, but this time the reverse: start by playing the whole of the LH, and drop the RH notes one by one. Once you can do both ways, you will have mastered HT for life!

Do not try this with the whole piece. Work in small passages, maybe one or two bars at a time. Bach fugues tend to be a nightmare to join hands. Try this method: it always work.