Choosing a safe tattoo studio could be the most important part of getting a tattoo. Having a bad tattoo for life, would be nothing compared to the posibility of getting a mortal desease.
The art of making a tattoo consists of injecting ink under the upper layer of the skin (dermis) with a needle. This needle breaks the skin structure and opens a wound that produces bleeding. This process leaves an open channel for infections, for which the tattoo aftercare process contemplates the sealing of the affected area for a couple of hours and the use of special soaps for regular cleaning.
But the worst risk doesn't come from infections. There's a number of blood transmission deseases (HIV, hepatitis, siphilis, tuberculosis, etc.) that can infect your body if the tattooing elements are not correctly sterilized/disposed. If the needle, for example, was in contact with contamined blood and is re-used in a healthy client, the desease will be transmited to the new host.
There are two types of elements a tattoo artist uses in order to print the tattoo under your skin: disposable and non-disposable elements. The disposable elements must be thrown away once used. Non-disposable elements must be correctly sterilized using autoclaves. Autoclaves are machines designed to take surgical elements to high levels of temperature and pressure, killing all blood born patogens.
So, when you enter a tattoo studio for the first time you should ask yourself "how clean is it"? Make a visual analysis, check the floors, the corners, the smell. Ask to use the bathroom and see how clen it is. Many times if the bathroom is shiny you can trust they take good care of the hygiene of the rest of the place too.
An important thing you should look for is the autoclave. An autoclave is of vital importance in the hygiene of a tattoo studio. If they don't have one, turn around immediately. If they do, you still don't know if it's working correctly. A regular analisys should be carried out and the samples displayed to the clients. Ask for them!
Another thing you should see in the working area is a biohazard container to receive those disposable elements that got in touch with blood or fluids and therefore are no longer usable.
Depending on the country/state regulations there's a set of rules stablished by goverments to ensure certain level of hygiene. Search for these regulations and see if the studio complies with them. Many times, studios must undergo quality/hygiene investigations or aprooval processes. Certificates are given to those studios that succeed and usually they are displayed proudly in the walls. Check for them.
In addition to the previous analisys other things must be supervised once the tattooing process begins. All disposable elements must be disposed after one use. This means they must be open from their hermetic package only once they are going to be used. Ask the tattoo artist to open them in front of your eyes. If he/she is committed to the hygiene in the process he won't have any problems in doing it.
The tattoo artist must be wearing latex gloves (and have non-latex gloves available for alergic people) at the moment of tattooing and clean correctly the area before inking.
As a last advice, see other regular conducts in the staff working there. If, for example, you enter the tattoo studio and see they're tattooing a minor (against the law in most places), you can surely spect them to oversee other regulations, like those concerning to hygiene.
Check carefully, look closely, ask a lot, and you'll surely avoid the risk of getting into trouble.