The first enemy always turns right when leaving the holding pen, so heading to the left is generally a safer initial move. (But note that all other enemies turn left when leaving the holding pen, both at the beginning of the level and when re-emerging after being eaten.)
Eating power-dots and then eating enemies is a good way to get extra points. But power-dots are also useful for clearing a good deal of the maze without having to worry about being pursued. Learn to balance these two uses of power-dots.
Remember that enemies return to the holding pen and become dangerous again even if the power-dot hasn't worn off. Eating enemies right near the exit from the holding pen is very risky.
If a portion of a given maze is more difficult to clear of dots, clear it first (during the grace period) when you aren't being pursued.
When the enemies are pursuing you, you can use this pursuit to get them in a row behind you just before you eat a power-dot. You can turn on them and eat them without having to chase them very far.
When you eat a vulnerable enemy, the game pauses for a moment. You can use this pause to change direction, by hitting the appropriate direction key during the pause.
The enemies slow down in the tunnels that wrap-around from the left to the right sides of each maze, but you keep going at your normal speed. Therefore, these tunnels are very useful to shake an enemy who is right on your tail.
As the levels get higher, the enemies' speeds increase faster than yours, so getting an enemy on your tail becomes more dangerous.
Remember that the Invisible power-up doesn't make you invulnerable, it just keeps the enemies from chasing you. You can still lose a life if you run into one of them!
Try to time your movement through the maze so that you're close to the power-up when it appears. Note that going after a power-up isn't always the right decision to make; for example, if it takes you more than 5 seconds to get to a 250 Point power-up, you'll lose more points in lost time bonus than you'll gain from the power-up!