Use your mouse to draw the shortest lines from start to finish in as little an amount of time as possible. Watch out for walls, draw through mazes, and keep up with complex levels with only three lives to spare; losing one each time you hit a wall.
Most drawing games you'll play online are sort of difficult to pick up, but aMaze is one drawing game you'll be able to master within seconds. The object of the game is to draw a line from start to finish in the shortest amount of time possible. That's all you have to remember.
Once the game starts, you'll see how difficult it can get. The first level as no obstructions while the second has a few, then the occasional maze, then levels that will take some time to carefully draw through. You're only given three lives at the start of the game, too, and you can lose a life very easily by touching any wall, even a little bit. Although the first levels you'll come across are quite easy, later levels become more complex, and you'll have to think of how to complete them before you even start drawing.
If you have a lot of room to work with, go ahead and try as draw across the screen as fast as possible - for levels with mazes and labyrinths, go slow around corners and fast along straight paths. Having a slow computer or internet browser is one thing that can make this game impossible, so try turning down the quality in aMaze if your computer is having trouble keep up.
Besides those hints, this is mostly a game of skill - there's no way around it. If you're patient, and draw as quickly and carefully as possible, you should make it pretty far in aMaze. If you've ever played a drawing game before, you'll do fine in this game; but if you don't have a lot of patience, you'll probably lose your first three lives very quickly.