It partly depends on where in the world you are, but basically the way to start is to find a studio or a class near you and start taking lessons.
Depending on your goals, interests, and resources, you may want private lessons or you may prefer to start with much less expensive group lessons.
To find a studio (in the US), check the Yellow Pages, the directory on this site, and/or on accessdance.com. I strongly recommend you check out several studios before you make up your mind. Most studios have an introductory special where you can take a lesson or two for a fairly low price. Be aware that different studios have different pricing structures. Studios that are part of the big national chains (Fred Astaire, Arthur Murray) tend to sell lessons in fairly substantial "packages" of lessons, groups, and practice parties--find if that's what you want, but it's not the only way to go. Independent studios tend to be more flexible (and less expensive).
You may also find ballroom classes at local colleges, recreation centers, YMCAs, etc.
Welcome to ballroom dancing! Enjoy!