You can get curved wood several different ways.
One way is that you can cut a curved shape in a piece of wood. However, the grain has to be curved to get a strong part without grain run-out weakening the part. You can also have thin slices of wood that can be bent all by themselves and laminate them together over a form so that they hold their shape. You can also use a bath of boiling water to soften a piece of wood and clamp it on a form to hold it's shape while it dries. We've used a section of aluminum gutter with wood blocks sealed with silicone at the ends set over a camp stove! There are other ways as well, but the best way I can think of is to use steam.
Before I start in on this, be sure to use common sense and protect yourself from the steam - steam can give awful burns in a very short period of time as it holds a great deal of energy. Use gloves, goggles and protect bare skin. Be sure to know how to treat burns in case of an accident.
The hot water and steam work because they soften the ligning in the wood which binds the cells together. When the lignin cools, it "sets" holding the wood in position. Steam-bending is best accomplished by using green wood because of the moisture it contains, or air-dried wood that has been soaked before steaming. Kiln dried or treated woods don't work because the lignin has already been "set" by the treatment process. For steam-bending you will want to select your stock fairly carefully for straight grain so that it doesn't split out along the edges.
The process is best accomplished using steam as you need to maintain a temperature between 200 and 212 degrees Farenheight (93-100 degrees Centigrade) You need to have steam during the whole process. (i.e. you can't run out of water, and you can't add cold water to the boiler and "kill" the steam) You also want to remember the rule of thumb is to steam the wood for 1 hour per inch of thickness. This is, however an estimation and varies by wood species and . One thing you want to be careful of is to have the parts be wet throughout the process. When we steamed cedar ribs, we soaked them before the process and if we didn't put the ribs on the canoe fast enough, we'd have to wet them again with hot water on a swab so they didn't dry out and "heat treat". Once you take the steamed piece of wood out of the box with a pair of gloves, you need to work fast before the wood has a chance to cool before bent into position. It is good to support the outside of the stock with a metal band or to "stretch" the outside of the wood with your gloves to keep the part from splitting out along the grain.
Steam boxes don't have to be fancy affairs. You need a safe heat source that will continuously generate enough heat to provide adequate amounts of steam for the steam box. Propane fired burners such as those used for crab boils are common. If your heat source burns fuel, you want to have adequate ventilation or work outside to avoid carbon monoxide poisoning.
You will need a container large enough to hold enough water or be able to refill it somehow during the process. Ideally, you should be able to see how much water is in the container so it doesn't boil dry. The container should be tight, but not so tight that it builds up pressure and becomes an explosion hazard. New metal gas cans (UNUSED!!!), tea kettles and "Cornelius kegs" with the valve removed have all been used as boilers.
You will need a tube to route the steam from the container to your steam box. Radiator hose is commonly used. It's available from McMaster-Carr, and auto-supply houses among others for about $5/foot. You shouldn't need much as you want to keep this as short as possible to avoid losing heat in the tube.
Last but not least, you'll need a "box" to contain the steam. I've seen cedar boxes with loose-fitting end-caps. I've also seen plywood boxes with rigid foam-board on either the inside or outside. (Don't know how well it works on the inside!) Large boxes often have pigeon-hole like dividers to allow steam to circulate around many pieces. Another very common method is to use pipe - even plastic pipe. I'd avoid the traditional recommendation for PVC in favor of ABS pipe. PVC softens at about 140 degrees Farenheight (60 degrees Centigrade) and starts to degrade, structurally- not enough for steam! ABS pipe starts to soften at 212 degrees Farenheight (100 degrees Centigrade) and is a better choice. The ABS is commonly used as drain plumbing in houses and is commonly available. Like with the kettle, you want a little bit of the steam to leak out so that pressure doesn't build up. Also, you'll want to be able to slope the "box" so that condensation can drip down to a drain hole. Large openings are commonly plugged with rags to keep the steam in the box. Some boxes have holes in them so that only the part of the stock that needs to be exposed to the steam goes in them. There are many "custom" boxes - it only depends on your imagination.
The set-up below is the one we used at WoodenBoat. At some point in the future want to build one like this for steaming canoe and kayak ribs:
I have some long pieces to do for the kayak coamings, so I plan to work with two pieces of tubing. One with a single end cap so that I can soak the stock before steaming and another ABS one for the steam box. We'll have to see how it goes...