ToME: the Tales of Maj'Eyal

I am new and have extracted gems from equipment i've looted

however I cannot figure out how to turn them into alchemist gems

anyone mind sharing with me how to do it?

thanks

You should have a skill to do this, can't remember the exact name but it's something along the lines of 'create alchemist gems'.
If the game hasn't put it on your skill bar, press 'm' to bring up the skill list, and find it in there, then drag it to your skill bar.