While using a dehydrator is probably the easiest way to dry peppers instructions vary by model, but they all consist of some form of putting peppers in the machine and walking away there are alternative ways to dry peppers that are just as easy. Don't expect any method to take less than a few hours to do.
Oven Drying Method
One of the easiest methods to dry peppers is to put them in an oven. This method works in a similar way to the dehydrator. Set your oven to the lowest setting available. Arrange the peppers on a baking sheet in a single layer. Cut them in half and lay them cut side down if you want the peppers to cook for a shorter amount of time or if they are larger peppers. Put the peppers in the oven and leave the door open a few inches so that air can circulate through the oven. Leave them in for several hours or even days, depending on the pepper's type. Peppers that have thicker skins, such as serrano peppers and especially jalapeno and habanero peppers, will take a few days. Peppers with thinner skins such as tabasco and cayenne peppers will take only a few hours. Check them after an hour and then once an hour when you can to make sure the temperature isn't too high. If the temperature is too high, you will know because the peppers will start to get soft or blackened, which means they are cooking instead of drying. You do not want this. If you are using a convection oven, there is no need to leave the oven door open.
Microwave Drying Method
The microwave method is easy, but it takes a little vigilance because unattended peppers in the microwave have a tendency to explode. First, cut the peppers in half and remove the stems. Arrange them on a plate or microwave safe tray, cut side down. Turn the microwave on to the lowest setting possible. On some microwaves, this is the defrost setting. For the first minute, check the peppers every 10 seconds to make sure they're not cooking. After that, check the peppers after longer and longer intervals. This should give the peppers a brief chance to rest during the drying process, and reduce the chance that they'll explode. Expect the drying process in the microwave to take a few hours. Remove the peppers when they are wrinkled and leathery.
The Natural Method
There is a very easy way to dry homegrown peppers, although it takes a long time. Cut the stem of the plant and hang the whole thing in a cool, dark place, such as a garage or basement, through the winter months. In a few months, the peppers will be dried. Remove the dried peppers from the plants when they are ready. You can dry store bought peppers in this way as well. Just thread the pepper stems together with a needle and string and hang them as you would hang the plants.