A skill gem sits in a skill slot of its own, with 3 support slots beside it. A support changes that skill alone, and only skills whose tags it supports. A character has 6 skill slots. Gems and their slots are in the build planner before the game's own screen; in the game today every skill sits alone in its slot, at the highest gem level your character can use.
Every support
Numbers run in a straight line from gem level 1 to 20 and on past it. Supports' more and less multiply each other and everything else. Each support also multiplies the skill's mana cost.
Support
Attribute
Supports
At gem level 1
At gem level 20
Mana
Faster Attacks The supported attack is faster.
Dexterity
Attack
25 increased attack speed
44 increased attack speed
×1.1
Faster Casting The supported spell is cast faster.
Intelligence
Spell
20 increased cast speed
39 increased cast speed
×1.2
Multiple Projectiles The supported skill fires two more projectiles, each weaker.
Dexterity
Projectile
2 additional projectiles; 26% less damage
2 additional projectiles; 17% less damage
×1.5
Increased Area The supported skill covers more ground.
Intelligence
Area
20 increased area of effect
39 increased area of effect
×1.3
Concentrated Effect A smaller area that hits much harder.
Strength
Area
-30 increased area of effect; 35% more damage
-30 increased area of effect; 54% more damage
×1.4
Added Fire Damage The supported attack adds fire damage.
Strength
Attack
3 added fire damage (min); 5 added fire damage (max)
40 added fire damage (min); 60 added fire damage (max)
×1.2
Added Lightning Damage The supported attack adds lightning damage.
Gems go from level 1 to 30. Each level requires a character level, and a gem is as strong as a character of that level. Level 20 requires 70, as in Path of Exile; ours go on to 30. A gem's attribute requirement grows with the level it requires, like gear's: a single-attribute gem needs 5 + 2.2 × that level.