The first thing to consider when you are choosing a tuxedo is the tuxedo color. Traditional black is always fitting for any formal occasion. Lighter colors tend to be used for daytime occasions that are slightly less formal. Today, the color of the tuxedo tends to relate the "vibe" of the occasion.
After you've chosen your tuxedo color, look at the type of lapel that it has. Lapels come in shawl, peak and notch style, although today there are variations of these basics.
Tuxedo jackets come in a multitude of styles. Your color choice and lapel choice should have eliminated several of them. Tails or no-tails would be your next decision. After that, you should choose a style that you feel comfortable in.
Tuxedo shirts come next. Nowadays shirts can come in a multitude of colors. White, off-white and black are most common. The most common collar styles are the traditional wing collar and the lay down collar which looks like a regular dress shirt collar.
Your neckwear and vest style and color are next. Many times brides tend to want the vest and tie color to match bridesmaids dresses or a chosen color accent. The following are more common styles of neckwear. The bow-tie is probably most familiar and the most formal. The ascot is traditionally worn during daytime events and is an older style. The windsor tie looks like a business tie. The bolo has a more "western" feel and is normally worn with western style tuxedos.
Finally there are shoes. Today, shoes tend to match the tuxedo in color, but most are black. You can buy or rent these at your local tuxedo rental/sales business.
An alternative way to choose a tux is to go to a site like Jim's Formalwear "Build A Tux". There you can choose from available styles and colors. A word of caution. Sometimes colors are not exactly as seen on the website due to monitor color variations. Also textures are not as clear on the web.
I would suggest you use sites like this as a starting point and then personally visit your tuxedo shop and make your final decision there. A knowledgeable tuxedo shop will be willing to answer your questions in depth and help you make more confident decisions.
That's the process in a nutshell. Generally, your date or your bride will have an idea as to her suitable colors. Your job consists of finding a style that you are most comfortable with.
Happy tux hunting!