There are a couple of good ways to bend medium density fiberboard (MDF). One is called "Kerf-cutting" and the other is by laminating. For most purposes Kerf-cutting will work better--it's easier to pull off and less time-consuming. Laminating is the better way to go when you need to form a compound curve.
Mark off the section to be curved. For example, you have a 3/4-inch thick piece of MDF eight feet in length and you want to make a 30-degree curve over the middle three feet of the product. Line up your work on a table saw with a large support table and set the blade depth to about 19/32 inch.
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Cut into the MDF at 3/4-inch intervals on what will be the inside of the curve, making cuts from the left boundary to the right. Cut at 1/2-inch intervals for a slightly smoother curve.
Lay the MDF down on a flat surface, kerf-cuts facing up. Put a stop at one end so it doesn't slide around. Lift the other end up and place a board under it. Begin raising the board so that the kerf-cuts begin to close. Stop about half-way to the desired 30-degree curve and repeat the process at the other end.
Flatten the product again. Fill the kerf-cuts with white glue. You can use a stronger polyurethane adhesive, but If you use too much in the kerf, it will expand and straighten out the curve as it dries. Practice on a sample piece of kerfed MDF if you are doing this for the first time.
Re-form the desired bend once the glue is spread evenly through each kerf and either clamp it in place or support the undersides of the two raised ends of the MDF and put weights on the curved section to hold it down as the glue dries.
Use three sheets of 1/4-inch thick MDF to form a laminate rather than a single 3/4-inch sheet when you need to form a compound curve, one convex and the other concave.
Improvise jig stops at either end of the first 1/4-inch MDF piece (two gravel-filled packing boxes will do). Mark off both curved areas. Improvise a support under the convex section (a clamped down cardboard construction tube works). Use weights to hold down the center of the concave section and another support under the MDF at the outside and upper end of the concave section.
Add the second layer and force the two layers together. Then add the third layer. Clamp. If your improvised jig and clamps hold the three layers together well, remove the clamps to prepare for gluing.
Spread construction adhesive evenly across the upper side of your first layer using a notched trowel. Put this first layer back into the jig, adhesive side up, and temporarily hold it in place with clamps.
Force the second layer down onto the first, beginning at the most concave part of the MDF and holding the ends upward and away from the lower glued surface. Work from the center of concave curve outward and force the second layer down onto the first, unclamping the first layer and re-clamping both layers together as you work.
Repeat the process, adding the third layer of 1/4-inch MDF to the first two.