Opposition (together with outflanking) is no doubt the key concept to start off with in learning pawn endgames.
In coaching, I often use the numerous excellent exercises from Dvoretsky's Endgame Manual on the theme. The other day, I found two exercises in a book I came across, How To Reassess Your Chess (by Jeremy Silman), which are also great positions to learn about opposition through.
1. White to play - he wins if his king can reach f8, g8 or h8.
2. White to play - whoever gets the opposition (vertical or horizontal, close or distant [three or five squares between the kings]) wins. You can also throw in diagonal opposition as well, but just working with vertical and horizontal should be better.