I didn’t even know about the existence of “professional poker players” in the same sense it would apply to, say, golfers. Do they get sponsors rather than gambling their own money?
To get started, you use your own money. Once you get good, then the sponsors line up. Sponsors want their "employees" to advertise, and will line up professional poker players for most of the televised poker tournaments out there. Sponsorship may include flying the professional to the tournament, paying the entrance fee and paying for the initial stake, plus room and some food.
Not a lot, but better than going to a tournament on your own nickel.