They can either be wood or aluminum. I encourage you to use a wood one. If not, I will make fun of you like I do my good friend Bill Booker at LaSalle-Peru H.S. for using his aluminum one. If you choose the wood fungo, I would recommend taping the barrel. If you hit a good number of fungoes, the tape will increase the durability of the bat. I took the tape off of one once. The barrell was like sawdust, but I re-taped it and it was ready to go. One season, I figured it out, between the high school, American Legion, an junior high seasons I had hit over 10,000 fungoes. Tape it up!
First base fungo hits fly balls to center field (helps here if both fungo hitters move up and apart, hitting from about the front of the mound extended towards the bases). Center throws to second, second baseman is cutoff (for us it was, anyways - change to suit your style). Third base fungo hits balls to left field, who throw to third, with a second shortstop as cutoff (but you really don't need one, if you're shorthanded).
Many players "bone" their bats, meaning that before games, they rub their bats repeatedly with a hard object, believing this closes the pores on the wood and hardens the bat. Animal bones are a popular boning material, but rolling pins, soda bottles and the edge of a porcelain sink have also been used. Pete Rose had his own way of hardening his bats: he soaked them in a tub of motor oil in his basement then hung them up to dry.