To anyone baffled because the instructions in the description suck, you start out each level in build mode. In build mode you can place spikes to complete the minimum number required for the level (that's the numbers in the bar at the top of the screen), and you can even run through the level to test your build, but you can't actually complete the level in Build Mode.
To complete the level once you've placed enough spikes, press enter (or return, depending on your computer) to enter Play Mode and actually play the level. In Play Mode the spikes can actually hurt you, but you can now complete the level by touching the little fish guy at the end.