You park in parking lots and spots when you park to walk around Lake Eola. It is mostly pay as you go parking and during special events even more is available. Even business parking lots over on the east side of Lake Eola will have an attendant manage their parking lots. These are often the best buy.
On a normal day all three of these are usually available. Even very limited free parking. Then there is the other type which is use the parking spot and leave before a law enforcement officer tickets you for it. Hey, it happens and most have done it especially with street parking.
When I go to an event at Lake Eola Park I always get there early. During the fall it can take to long to find a spot even when extra lots are open. You may end up walking 2 or 3 blocks to get to the park. There are some condos which also charge non residents for parking in their parking garage. Usually these locations are relatively safe and run $17 to $20 for 4 hours or more. Not to bad for secure parking. Thornton Park condominium is one such place.
Downtown Orlando has quite a few small businesses. Most have metered parking in front of them but there are many on the eastern side with parking lots. I spoke of these above. You can still pay with your debit card and usually get an immediate receipt. During the Orlando Farmers Market I usually will use these and will get them for just $6. Get there early and maybe even get under shade or an otherwise perfect spot.