You should at very minimum be a certified diver. Specialty dive training such as search and recovery might be helpful as well. Equipment would be mask, fins, regulator, BC, weights, tank. Wetsuit would be wise as you likely spend a lot of time in the water hunting golf balls.
Practical requirement would be permission from the golf course. You wouldn't want to be hassled for tresspassing even if the course is a public course. Many golf courses already have arrangements for divers to collect golf balls. Also would be wise not to dive where alligators are nearby.
good luck.
A full wetsuit is the bare minimum. Crawling in that goo with pine cones, fishing lures, bullheads, leeches and all other sorts of creepy-crawlies without a suit is likely only done once. I almost never use fins. Very large lakes or ponds with plastic lining are the exception. You have to be pasted to the bottom and dig in the silt to find balls, so the fins just get in the way most times. You'll also need collection bags. I recommend they attach with a quick release mechanism or at least something that will easily break away encase of entanglement. (or if you have to run because you forgot to get the wisely mention permission or weren't wise enough to avoid alligators) j/k