Skinny people get the BEST muscles (largely because they're not obscured by a layer of fat, so especially abs). I wish I had your problems!
But you do have to work out and get enough protein, and that means strength training. At a minimum, push ups, crunches, planks and squats, with rest days in between. No equipment required! Past that, you could expand with a set of hand-weights for arm work (bicep curls) and an exercise ball for your crunches and plank. (very cheap) You could also add pull-ups for back work.
There are a lot of online programs that will ramp you up gradually. For example:http://hundredpushups.com/