1. Run distance and sprints. Using a stationary bike and/or treadmill can help with the distance. A long hallway in a school is good for sprints.
2. Master your leads. Indoors is great for practicing your leads off each base. All you need is one base and pretend its whatever base you need. Get comfortable with the distance of your leads until you don't have to look at the bag as you are moving off. A good base runner never has to look back. He knows how far off he is and where the bag is.
3. Master your starts. Spend a lot of time on your jumps at first base, especially if you are a base stealer. This can be a little tough on a slippery gym floor or hallway so you may have to improvise with your traction. Work on your second base starts as well using a walking-lead-then-sprint technique.
4. Read as you run. This technique works best for longer sprints or base running on a field but it can also work in a long hallway as well. Here is what you do. Pick out a sign, word, symbol, number, etc. somewhere down the hall and as you are running keep your eyes on the sign. This helps in two ways. First, it teaches you to run with your eyes up. Second, if your eyes are bouncing around a lot and you cannot read the sign well, your running technique needs to be smoothed out a bit - probably running on the balls of your feet more to keep your eyes still.
5. Use game-like situations. Incorporate the things you would have to do in a game. A hit-and-run is an example. After your quick start, look to your left for a second or two like you would do in a game to see what the batter did with the pitch and then continue your sprint. Work on your technique if you deviate from your line when you look in. To make this more challenging, pretend the ball is hit down the right field line. After looking in at the plate, turn your head to the right for a second or two to "see" the ball down the right field line. Then look forward as you continue to run. Great runners should not deviate from their straight line sprint even though their eyes are not looking straight ahead for the first few seconds.