The process is quite amazing and complex. The time it takes tadpoles to undergo metamorphosis to the adult stage varies quite a bit. Usually it can be anywhere from a few weeks to a few months, but for a few frog species (such as some bullfrogs) remain in the tadpole stage for up to 2 years. This is a good reason to be sure of what species you are obtaining as eggs/tadpoles.
The process of metamorphosis is complex and is a stressful time in a frog's life, especially near the end of the process. Externally, it starts with the development of back legs, followed by the formation of front legs. The frog's body shape changes as well. Many other changes, such as the development of lungs and the loss of gills, changes to the digestive tract (to accommodate the change from a herbivorous to carnivorous diet), and changes to the skin occur as well. Toward the end of metamorphosis, the tail is resorbed. Tadpoles may eat less during the last stages of metamorphosis, particlarly during the phase where the tail is resorbed.
As metamorphosis progresses, it is vitally important that the developing frog can easily get out of the water. Partially submerged sticks, wood and rocks can be used to make ramps out of the water (make sure they are stable), and it is a good idea to make a gravel slope out of the water to a land area. Lowering the water level in the container is also a good idea. Once the gills stop functioning and the lungs take over, it is possible for tadpoles to drown.
Some specialized ground species may need to be removed from the water altogether once their tails start to shrink, as they are not "programmed" to leave the water and may simply drown. Again, learn all you can about the species you are raising to give the frogs the best chance at surviving the process.
Feed the newly developed froglets small crickets, fruit flies, bloodworms, and other small insect and invertebrate foods.
If you have clearance to release native frogs, do it as soon as possible after metamorphosis, as close to where you found them as possible. This gives them the best chance to adapt to life as a frog in the wild.