All tattoo artists work differently in how they approach a project. Some are more comfortable with planning things out before your tattoo sitting, while other artists work better by designing on-site with you, and even drawing directly on skin to fit the piece to your intended body area.
A walk-in tattoo can sometimes be done that day, based upon the design requirements and the artists availability. In either case, be prepared for some wait time while your artist perfects the design for the final tattoo.
If you make an appointment, the amount of prior design and preparation time will vary depending on the complexity of the piece. If the tattoo is a portrait or art reproduction, then less design work may be required. If the piece is a custom-drawn design, then there may be more details and layouts to go over. Often, wrap-around pieces require more on-site drawing in order to fit the design to your body. Every design process can vary greatly, depending on the artist's method, and the type of tattoo that is being put together. Generally, it's a good idea to get the majority of the conceptual elements worked out beforehand, so you can maximize the appointment time for layout and tattooing.