I know. Simple, isn't it?
I'm 42 and have been doing press ups 6 out of every 7 days for the last few years. It's really easy. You start with however many you can physically do and work upwards. If you can only do 2, then do 2, take a break for five or ten minutes, do another 2. If you're watching a match on the tv, do a few every ten minutes. If you work in an office and can find some private space, do some every time you get bored. If you're a runner or a walker, drop and push out a few every couple of hundred yards.
I do a set, get on my iPad or read a book for a while, do another set and so on. You don't really sweat (unless you're really pumping) so there's no showers or kit involved.
Weight bearing exercise is extremely important, especially as you get older. For women, it helps ward off osteoporosis. For men, weight bearing exercise keeps up testosterone levels which keeps you all manly and sexy and whatnot. Press ups are also a quick, cheap alternative to joining a gym. Here is a list of the muscles that get a workout, off wiki.
While the push-up primarily targets the muscles of the chest, arms, and shoulders, support required from other muscles results in a wider range of muscles integrated into the exercise.
Primary muscles
Anterior and medial deltoids ("delts")
Triceps
Pectoralis major and pectoralis minor ("pecses;)
Secondary muscles (synergists or stabilizers)
Rhomboid major and rhomboid minor
Erector spinae
Rotator cuff
Posterior deltoids ("delts")
Serratus anterior
Rectus abdominus ("abs")
Transverse abdominus
Gluteus maximus ("glutes")
Quadriceps ("quads")
How to do them properly? Here's a clip from the Ellen Show where Michelle Obama and Ellen have a contest.
http://www.youtube.com/v/tiwgo3XleyENeither of them are doing it right, but Ellen is better. Here's the proper way.
You should be grazing the floor with your nose and your crotch, basically.
So there's no excuse. Anyone who has access to a floor can do press ups, they are good for you and they make you look and feel better.