After researching the appropriate fields, you will find yourself able to craft a levitator using the pattern at the right in an infusion altar, assuming you have a wand with 50 or more Vis in the altar, as well as a source of 8 of each of Volito, Solum, Machina, and Motus aspects.
Here's a video that shows you how the Arcane Levitator works: http://www.youtube.com/watch?v=G2JW8RbVSEM
Requires Research: Unified Thaumic Field Theory
After placing the item in the world, it begins to function immediately - any entity standing on it is propelled upward to bob casually at ten blocks above the levitator. Unless you happened to place more than one down. For contrast, compare the effect of seven levitators, as seen on the right.
Aside from flight, as it says in the Thaumonomicon, any entity that is falling beneath the Levitator will experience a controlled descent for 10X blocks, where X is the number of Levitators in the stack above the drop. For instance, Having a 7-high stack will propel you upwards for 70 if you were to enter the airspace above it, while entering below would set you into a slow fall for 70 blocks. It is important to note that the slowing effect is not an unlimited range, and as such no Thaumaturge should attempt to drop down a gap with insufficient levitators.
It should also be noted that the top side of the levitator will not instantly reset your fall so much as accelerate you upwards slowly. That means that should you attempt to stand on a 7-high stack of Levitators and attempt to get back down safely by hopping in and out of the area of effect (as one might do with ladders for quick descents), you should be careful not to stay outside of the lift for too long, else your momentum may still cause injury and/or death upon landfall.
From the ThaumonomiconEdit
While not true flight, the Arcane Levitator is the next best thing.
When placed the levitator lifts any item or creature above it up to 10 blocks into the air. Anything below the levitator is slowed enough to negate falling damage. Doing so costs a small amount of vis drawn from the nearby aura.
Each levitator placed upon another increase the range at which it can lift or slow entities by 10 blocks, so a stack of 3 can lift entities up to 30 blocks.
Levitators can be deactivated by applying a redstone signal to them.