How do you teach students to count for piano?For beginners I usually write in the count for them, making sure to put the numbers in the correct place under the rhythms. For instance, if the measure was half note - quarter - quarter, I would put 1-2 by the half note, 3 by the quarter, and 4 by the quarter. I tell my students they are supposed play when they say the number underneath the rhythm and to hold the note if more than one note is under the rhythm. This is pretty easy and simple concept to pick up. It may take them a few tries or you tapping and pointing at the rhythms, but the "lightbulb" usually shines in a few minutes. I do this until they can count without mistakes, then I have them count with out having numbers written in. If they have problems I right them in, but my goal is to not have to write the numbers in. If there are any new rhythms I of course write in.
If it's just one line, that's one thing. But with different rhythms in different hands.... then what?First do hands separately ( clap, tap, or play) then do hands together. No matter what the rhythm the count in each measure is the same. You may have to point out, no this note is not played on the 2 but the & after the two.
What counting system do you use?Piece with all quarters -- 1-2-3-4 (course this depends on TS)
Piece where the smallest beat is are 8th notse -- 1 & (and) 2 & 3 & 4 &
Piece where the smallest beat is are 16th notes -- 1 a & a 2 a & a
Piece with triplets (simple pieces\rhythm) -- tah-tay-ti or tri-pel-let
For complex rhythms such as:
eigth notes vs. triplets -- hot-cup-of tea -- both hand play on hot => triplet -- hot-cup-tea and eigths -- hot-of
Very complex (And I think my method is a little complex too) = I use math, GCF I think. The short version, I find a number divisable by the rhythms (ex. 16 or 15) then I right in the count... I can't find my Khutcharian so I can't explain it more than that without making my head hurt. (long day teaching music to wonderful and lovely children

) But of course beginners don't need to no this...
But numbers work very well.
How do you handle two different rhythms in the hands?I think I said this above, hands separate then together. If the smallest note value is in the left hand, then count for the smallest note valeue. And this goes for any song. Even if there may be one sixteenth or eighth note, then I make them count for the 8th or 16th. It's good practice and when they get to that note it will have the correct tempo.
What about rests?I usually have the students say rest for quarter, rest rest for half, ect when they first learn about rests or have problems. I also have them count the rests too. In either case, I remind them to lift their hands before they say rest.
What about notes held for a long time?Then they must beheld for a long time!!!!

. For tied rhythms, I always ask how many beats you are supposed to hold it for then practice it, if necessary.