Tipping in the service industry is customary. In the US, this is usually about about 15%. Many people have their own ideas, less or more. I've spoken with people from other countries, and some countries don't tip, or tip less.
A lot of people mentioned bringing non-cash tips.
A good rule, whether an owner or someone who simply works in the shop does it, is what the tattoo is worth to you. If it was agreed upon to be a $300 job, and you feel it's worth $350, doesn't matter who does it. If you feel you got ripped, talk with the artist how to fix it, leave a standard tip to part on good terms if they're amicable. If they're rude and refuse to consider further discussion, then leave without tipping and never return.