Yes, you can make your own compost easily without much effort. You need four things for compost to form. (1) Air, (2) Moisture (Water), (3) brown material such as leaves, twigs, shredded cardboard pieces, shredded newspaper, (4) Green materials such as fruits peels, vegetables peels, grass cuttings.
The brown to green ratio should be 30:1 or if you go by weight it should be 3/4 of brown material and 1/4 of green material. You can make a pile which should be at least 3 x 3 x 3 feet in length, width and height. You have to layer your pile with one layer brown material and then one layer green material on top of one after another until you reach 3 feet in height.
Another method is to buy or make a compost bin made with holes on the sides and all around and put your brown and green material inside the bin. Then mix with either turning the bins or with a stick or garden fork. You will need to water the compost pile or compost bins every week depending on how dry it gets. The compost should not be too wet either, it should just feel like a wrung out sponge and not dripping wet.
Compost pile gets done much faster because it gets hot and cooks faster but then there are those insects and worms mixed with the finished compost. With Compost bins, the finished product is much cleaner without much insects and worms getting into it but then compost bins takes much longer to complete because it is cold composting taking place inside the compost bin. You are looking at two months for hot compost pile whereas using compost bin will take about six months to a year.