How can I level my bed?
This really depends on the degree to which the bed posts are out of level, the floor type you are using and the diameter of the post contact on the ground. 

It sounds like you are going wood posts, what I would do there is to get a few Cork or rubber Adhesive floor protectors (like below) 

The problem there, is that you need to find material which is slightly thicker than your gaps, since you cannot really add these things together too much (since they will be easy to fall off) - You can also attempt to slit them with a long stanley blade. these strips will needed to be applied to the underside of each bed post.