I've checked wikipedia and it didn't have any specific information, and I've googled a number of permutations of words like tattoo, 1800s, method, ink, needles, tools. I also checked the tattoo tag on this comm, and while one person asked a similar question, I'm looking for less haphazard tattooing methods.
I need to know things like what kind of tools might be used and how, and if there are any limitations on colors of ink that could be used. I'd also be useful to know if this character, who is a professional and accomplished artist, could make a really nice looking tattoo if she's only done it a few times before (it would be a fairly simple and small tattoo).
eta: Thank you very much for all the replies! They have been very helpful. I think I have some ideas to go on now, although if anyone else has info to add, it would be most welcome.