In Path of Exile, you use skills by putting them in sockets of your equipment. There are 4 socket colors in Path of Exile – Red – associated with Strength, Green associated with Dexterity, Blue – associated with Intelligence, and White.
You can change the color of sockets on the item by using Chromatic Orb on it. Red, Green, and Blue are socket colors that you will encounter all the time but white sockets can be found on some unique and corrupted items.
And below you can see an item with 3 sockets where 2 of them are linked together – active skill gem is not supported by support gem because they are not linked together.
Let me note, that main color of the sockets on items is biased towards its base type and attribute requirement to equip the item – armour items (associated with strength requirements) will most likely roll red sockets, evasion items (associated with dexterity requirements) – green sockets and energy shield items (associated with intelligence requirements) – blue sockets.
It also applies to weapons, for example, claws are intelligence and dexterity based, so they will most often roll green and blue sockets when colored with Chromatic Orbs. If a claw has 50 dexterity requirement and 70 intelligence requirement, blue sockets will be rolled more often.
The same principle applies to all weapons, and to see which color sockets you will roll most of the time, you just have to check attribute requirements on the weapon.
Skill gems can be socketed in sockets of their corresponding color – for example, you can put green gems only in green and white sockets (White sockets can have a gem of any color socketed in them).
The maximum amount of sockets one item can have is 6 (Only two-handed weapons and Body armors can have 6 sockets), so naturally, 1 active skill gem can be supported by 5 support gems. However, for active skill gem to be supported by support gem, sockets that they’re in have to be linked together.
Hopefully the above guide will be helpful to you.