A really great practice spread is the Daily Spread. Basically you pull cards to see how the next day is going to go.
It's very effective as a learning tool for a few reasons: it's fun, immediately gratifying (don't have to wait to see if you're interpretation is right), your reading yourself so you can do it at your convenience, and you can analyze how accurate you were while the events you tried to predict are still fresh.
Make a three card vertical line as follows:
4. LATE EVENING (Optional: for Night Owls & Musicians!)
SUMMARY (separate from the rest)
Once you've created this three card vertical line, start layering. If you're new to layering, try just adding two more cards to each position. Place them horizontally, so you end up with three cards for morning, three for afternoon & three for evening.
Write your spread for the next day down or take a picture of it on your cell phone. The next day before going to bed, take a look at the cards & think about what happened during and analyze what the cards were trying to tell you.