The Republic or Imperial fleet. You know, the big space station you go to at level 10 or so.
Artifice requires gathered materials (from Archaeology) and mission-derived materials (from Treasure Hunting). If you want to be a successful Artificer, you'll probably want to have those two skills! The basic items only require the gathered materials, but they're not much good. Instead of using the basic items, craft them and then reverse engineer them (using a little button on your inventory panel) for a chance to get a better version of that item. The better versions will require mission materials, but they're well worth it.
To acquire gathered materials, go out into a questing area (assuming you're at level 10 or so, go to Coruscant if Republic and Dromund Kaas if Imperial) and look for crystal formations and archaeological finds, which will be marked on your mini-map with little asterisks. Right click on them to gather. Alternatively, you can pull up your Crew Skills tab (hotkey: n) and send a crew member out to find some Archaeology materials. (For lightsaber crystals, you'll need Color Crystals and Power Crystals, which are derived from different missions and gathering nodes.)
To acquire mission materials, pull up your Crew Skills tab and send a companion out on the appropriate mission. As the name implies, mission materials can only be acquired through missions and cannot be found lying around in the game world. (For lightsaber crystals, you'll need Gemstones.)
From an experienced and obsessive crafter to a newbie, good luck!
This was really helpful, thanks a lot!