Skill Gems I
Skill Gems I: The Basics
In Path of Exile, all of your skills (other than your default attack) come from items called 'skill gems'. Skill gems must be socketed into your equipped weapons and armour in order for you to be able to use the skill they grant. It doesn't matter which item the gem is socketed into, but the socket has to match the colour of the gem. In other words, red skill gems can go in red sockets, and can't go in blue or green sockets. Support gems work very similarly to skill gems, except they don't grant you a skill by themselves. Instead, support gems can augment the skill gems they are linked to. Not all skill and support gems work together; You can't use a 'Melee Physical Damage Support' with a spell, for example.
For a support gem to properly augment a skill gem, both the skill and support gems must be socketed in linked sockets. If they aren't linked, the support will have no effect. You can tell whether or not your support gem is affecting your skill gem by looking at the on-screen skill icon. Properly linked support gems add a little letter to the skill icon on the user interface. Most support gems also change the mana cost of the skills they're supporting.
You can add or remove your skill and support gems at any time, so don't be afraid to experiment with strange gem combinations.