Just wondering how I can extract artifacts from a planet.

you either using an artifact to extract an previously built artifact structure from planet structures
or if you mean how to collect your artifact production - check in game:
tab TRADE - see Planetary production output - see line Artifacts xyz points / hour and next to it button Receive Artifact shipment. Eventually with higher production, you will see a great new button to mark: All - this will help you to collect artifact production in bigger volumes and receive better items.

^^ Yes, if you mean COLLECT the resources from your planets, then you go to the appropriate tabs.
If you mean there is an artifact on a planet and you want to put it back into your cargo hold, you have to use one of these:

Mylarai Build Extractor
Allows extraction of 1 special structure from a planet, so it can be built elsewhere.

They cost 10 energy to use. You get them from hunting the NPC.

I wish I had as many as you. I'm always at around 3-4 of them.

Probably means my planets aren't running as efficiently as yours. Hahaha.
I loath going back over my rocks every month and moving stuff around; even though I know it would be better to take it off of the 10x and put it on the 15x. I tend to use more of them after I invade a planet. If it is a good but marginal planet, then I might just strip it bare and take my chances on defense. If it is an awesome rock, it gets the flux of course.

Thanks guys