I've never hunted rabbits where you live, but I hunt alot of them here in Wyoming. From what I hear, things over your way are alot more crowded and bushy. Out here things are pretty open, but even around creeks and such where things are close I still limit out if I want to. I just walk them up by myself. I took my dog out a few times, but that didn't work out so well. I almost always hunt by myself, and with usually with a 10/22 .22lr, but I have hunted with 32/20,223,44spl,38spl,45 acp, 308win and my new one is a ruger mark II.
Just go out and start walking, but walk really, really slow. With the openness of the areas I like, you can jump them and may still get a standing shot after they run 20 yards or so, but if the area that you hunt is so tight that you won't see them after 20 yards, you have to get a shot before they bolt. After the first few days of the season, you will get to the point that you can spot them sitting before they run and will then be able to make clean head shots all day long.
One tip though, hunting rabbits like this will teach you to shoot offhand. If you spot a rabbit, chances are that he has already spotted you and is watching you intently deciding to run or to let you walk past. If you see him and stop, which you normally will, shoot him where you stand. The minute you move in ANY other direction than what you were when you stopped, he will bolt. Do not try to take a knee, move back to a handy tree or attempt to get closer, shoot him right then and there and be quick about it or he might think that you are going to shoot him and run.
Joe