A lower level gem needs to be socketed first before a higher level gem can be socketed. For example if players want to socket a Lvl. 8 gem, they must socket all of the previous gems in order (beginning at Lvl. 1) into the equipment first.
Gems can be obtained from the lockbox dropped by the Wanted List bosses, or be quickly obtained from Appraisal (which costs Cheddar). There is a good chance to obtain high level gems from Appraisal. Gem Shards can also be obtained from events and then exchanged with Muenster for Lvl.7, Lvl.8 gems.