When learning a new piece there is one pitfall that I discourage students from falling into. People of all ages lead busy lives. Finding practice time to learn pieces can get tricky. As I explained in the first tip, developing this habit is of utmost importance.
The pitfall I see is this: student begins playing piece, gets a few measures in, makes a mistake. Students stops, and goes back to the beginning, playing the same thing they just played, gets to that same place a few measures in, makes the same mistake, and then....did you guess? Goes back to the beginning. So what portion is being practiced? The part they already can play well!!!
My instructions are always: stop. Go to the place a few measures in where the problem happens. S-l-o-w it down. Employ one of these ways to fix that problem area:
1) Again, slow it down
2) if piano, try playing hands separately first
3) Methodically strip and rebuild: example in 4/4 time: play beat 4...a few times (x amount of times correctly), back up and play beat 3 and 4...then beat 2,3,4....and finally the entire measure. I call this "practicing backwards"
More tips to come!