If you're looking for bodyweight exercises that you can do at home then you need to look for compound exercises and some isolation movements.
Compound exercises are exercises where you need to move more than one joint if you want to do them properly. This kind of exercises are the most important ones. These are the best and most known compound movements: push ups, squats, lunges, pull ups.
Combine these exercises in a routine. For instance: 10 push ups, 15 squats (or jumping squats, which are heavier), 10 lunges per leg, 10 pull ups if you have something that can act like a pull up bar. Repeat the same routine twice again but always do 8 reps instead of 10.
Finish of the workout with some cross crunches and the plank position.
Try to mix things up from time to time. For instance, do push ups with your hands wide or with your hands just next to your chest or maybe in a diamond position next to each other just below your chest. The closer your hands are to each other, the more stress it puts on your triceps.
Give it a try, you don't need any equipment for this one and I'm sure you will like it.
This is just one basic routine I just put together for you. You can find more of these on my website.