For starters, we should clarify just what we’re talking about when we say fungo bat. Longer, lighter and thinner than a regulation bat (but a larger barrel), a fungo bat is typically 35 to 37 inches long, and weighs between 17 and 22 ounces. As David Allison wrote in the June 1978 edition of Country Journal, “A fungo bat looks to be a cross between a baseball bat and a broomstick.”
Though entertaining enough, this play appears in its entirety as a small part of Sorrentino's magnum opus MULLIGAN STEW. You can read it as easily there as in this form. Plus you'll have the rest of Mulligan Stew as well. So I recommend you only buy this volume if you're the sort of collector who owns books because of what they are, not what they say.
To figure out who shoots first, players usually throw or roll a baseball to a certain object (usually at close range) and whoever is closest shoots first. The first person then gets to choose the first hole and tees off. To tee off (and for most shots) players hit the ball like they were playing baseball, but depending on the distance from the hole the player may choose to ‘putt’ the ball instead of hitting it. To putt the ball, the player places the ball on the cup (the end of the fungo bat), and can toss the ball from the cup in hopes of getting a more accurate shot. In shooting or putting, the player must have one foot where the ball landed during the entire duration of their swing or putt, failure to keep the foot planted results in a loss of a stroke. Scorekeeping is identical to traditional golf; the player with the fewest strokes essentially wins the hole. Players traditionally play nine or eighteen holes of fungo golf, and at the end the person with the fewest strokes in the set number of holes wins the game.