It's extremely simple, you just wire it in parallel with the relay coil (or whatever inductive load you are powering). You must have the diode so it is "blocking" and not forward biased. Forward biased simply means the diode conducts with little resistance to the current flow (almost like a short circuit). But turn it around the other way and it blocks the current. So basically it's like a one way valve and when the relay is powered by DC current the diode is doing zippo because it's not conducting, i.e. the "one way valve" is in the blocking direction.
When you turn off the DC power to a relay / solenoid / inductive load, the electric field of the relay "collapses" and in doing so it generates a voltage which is the opposite polarity of the DC power. The flyback diode allows this reverse current to flow thus preventing the reverse voltage from building up and damaging something.
Google "Flyback Diode Relay / Inductor / Coil" and you should get loads of hits with diagrams and explanations. A flyback diode is not a special diode, it's just the name given based on the use it's being put to.
Example the same basic silicon diode could have various names given to it depending on the use:
Flyback diode
AC rectifying diodes
Auctioneering diode
Keith.