A tattoo is a permanent body decoration, so it's important to consider the type of infinity design. Depending on personality and aesthetic tastes, there are many styles of infinity symbol to choose from.
One of the best ways to choose a tattoo design is to look online. Many tattoo websites have lots of example designs that can help you figure out what styles you do and don't like. While you might want to go with a traditional infinity symbol, you could do a double infinity, a floral infinity or a tribal infinity design instead.
Once you have an idea for what type of style you want, talk to the tattoo artist and personalize the design. You might have the exact design already drawn out, but many people choose to personalize their tattoos and have their artist draw something up for them. You can bring in sketches or pictures for inspiration, and the artist can draw a design for you. From there, you can tell the artist what you like, and what you want changed in the design. Don't be afraid to have him change something – remember, this is going to be permanent. Once you have the final design, it's time for the inking.