In Scooby's opinion, pushups are the #1 best exercise you can do! They are simple to do and are a great upper body workout for the complete beginner or the advanced bodybuilder. You can get a complete upper body workout by combining these pushups with crunches and pullups, all of which can be done easily at home.
Start by doing knee pushups. If you can do more than 20 of these then they are too easy for you and you should do full pushups.
You want to start slowly to avoid injury, the first two weeks you will only do this workout once a week: do as many pushups as you can without rest (a set) rest 2 minutes repeat two more times (three sets total)
If your joints and muscles feel ok, you can slowly increase the frequency and duration of your pushup workouts until you are doing pushups 3x/week for 20minutes. When you get to the point where you can do more than 20 pushups in all your sets, then its time to move on to a more advanced workout.