A free floating rail is attached only to the upper receiver and has no other contact with the barrel. This may improve accuracy by preventing stress placed on the barrel by a sling, bipod, or any other contact. Its the same concept as floating the barrel on any other rifle.
A non-free float usually drops in in place of the stock handguards and is held in place by the (D ring, Delta Ring, Slip Ring, whatever you want to call it) at the back, and a cap at the front. These are usually cheaper but as with the normal handguards they may move around a bit, depending on the design, and they do transmit force to the barrel.
As for installation there are many systems on the market. Usually non free float are a simple drop in with no tools required while many free float systems require you to remove the D ring and barrel nut with some specialized tools. An exception is the Daniel Defense Omega rail which is a free float that installs with a screwdriver and an allen key and requires no gunsmithing.
Hope that helps