Start at the end
by Ella Glasgow
I learned years ago, from my old piano teacher, to start at the end when learning a new piece. This fits in with your tip about practicing in sections. You start with a small section at the end and practice until it's comfortable. Then add another small section before that one. Practice the new small section, then play both together. You keep doing this until you've done the whole song.
The cool thing about this is you'll know the end of the song really well. How many times have we been to a recital where the child playing starts off really strong, but it all falls apart toward the middle and the end is all but lost. With this method, even if the beginning is a little shaky, by golly, the end will be superb!
Now that I'm a vocalist, I use this same method to learn new songs. It takes my memory factor way up to 11:)