You can effectively do bodyweight workouts at home doing some of the stuff that others mentioned and see results. That will only take you so far, eventually you should get a gym membership.
If you start using weights or dumbbells, work on form.....that is THE most important thing. I see a lot of people in the gym lifting heavy weights and they have terrible form, namely squats, barely anybody I see is doing squats correctly. I just wonder how they haven't gotten hurt yet. And warm up and stretch, probably the second most important thing.
Whatever you end up doing, keep on a routine, but switch it up from time to time, do different excercises to keep it interesting.
Have a look at this site
, there are quite a few exercises there that don't require equipment, or you can get a stability ball and do some of that stuff, there's quite a bit of that on there too.