If fungoes are a ball tossed into the air by a batter and then struck as it comes down then a fungo bat is a baseball bat used for hitting fungoes. To go into more detail, a fungo bat is a long, lightweight baseball bat used by coaches (or parents) during pregame hitting or practice to help them hit grounders and pop flys with more consistency and less fatigue. To be one of the best in baseball, countless hours of practice are a must and fungo bats are intended for both infield and outfield practice. Plus, they help tremendously with control and accuracy so that coaches and parents can place a ball where they want when they want. 
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!
To practice throwing around the infield, Bates recommends several drills you can use. The first involves placing four fielders in a square, about 15 feet apart. The players flip the ball underhanded to each other, like in a double play. Keep their arms straight, using a stiff wrist, with gloves on their hips once the ball is out. Every fielder follows their flip, glove side first, rotating around the square. The idea is to have a sequence of catch, flip and follow. The ball should be caught with two hands, palms open. After about two minutes, repeat the process rotating the other way for another two minutes.
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).
While many people view the fungo bat more as an antique piece of baseball’s history, there’s no doubt that it still has a special place in the modern game. Actually, the bat is starting to enjoy some revival all-round the game. Regardless of minimal production of fungo bats, you can rest assured that they’re here to stay. The bats are too beneficial to both coaches and players on a daily basis.
A baseball bat is a smooth wooden or metal club used in the sport of baseball to hit the ball after it is thrown by the pitcher. By regulation it may be no more than 2.75 inches (70 mm) in diameter at the thickest part and no more than 42 inches (1,100 mm) long. Although historically bats approaching 3 pounds (1.4 kg) were swung,[1] today bats of 33 ounces (0.94 kg) are common, topping out at 34 ounces (0.96 kg) to 36 ounces (1.0 kg).[1]
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Fungo bats have been around since the beginning of baseball and as most of us may know, baseball was said to be invented by Abner Doubleday in Cooperstown, New York during the summer of 1839. Since fungo bats were much easier to swing and gave off a ton of pop, they were almost seen as cheating back in the day. In a book from 1897 named "The Technical Terms of Baseball," the sportswriter Henry Chadwick stated,"The weakest batting is shown when the batsman indulges in fungo hitting." It wasn't until baseball bat regulations came around that fungo bats were only used by coaches and parents. 
This sounds like a lot of information, but with a little practise on the coaches part, it runs quite smoothly. Two to three reps per player in the field per section is quite adequate, and with 14 men on the field, this whole routine should take about 7 minutes. It's quite snappy, and quite impressive. I had many a parent marvel to me after witnessing it - "you look like a professional team!" I wouldn't try the routine with anything less than a 14 yr old select team, but with the talent to do it right, it's fantastic.
While many people view the fungo bat more as an antique piece of baseball’s history, there’s no doubt that it still has a special place in the modern game. Actually, the bat is starting to enjoy some revival all-round the game. Regardless of minimal production of fungo bats, you can rest assured that they’re here to stay. The bats are too beneficial to both coaches and players on a daily basis.
It is not clear why pregame infield fell out of favor in the majors. Today, coaches hit balls to infielders and outfielders during batting practice. Most players go at it leisurely, lobbing balls back in or across the diamond. That rankles old-school players like Jerry Kindall, a former major league infielder who coached Arizona to three N.C.A.A. titles before retiring in 1996.
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.”