Once you're a licensed attorney, it's real easy to become a private defense attorney. Just hang up your Dewey, Cheatem, and Howe shingle and you're ready for business. Of course, getting business is the hard part. Defense attorneys have to get their names out, which is why some opt to join Mega Law Firm, LLP's criminal defense division. Becoming a prosecutor requires the extra step of getting a job at a local prosecutor's office, where you'll steadily work your way from misdemeanors up to serious and violent felonies.
You might be able to get your feet wet in either criminal defense or prosecution as a law student. Depending on your law school's clinical programs, you could find yourself trying real cases as a part of a public defender's or prosecutor's office. If you really impress them, they might even hire you when you graduate from law school. Just keep in mind, though, the noontide of lawyers that make up the surplus in American markets today. They aren't at the bottom of the sea—they are the sea.