I joined a gym when I first began, as it was winter and I wanted to have a comfortable place to walk. I went about 5 times per week and just walked on the treadmill at first, nothing fancy. About a month in I decided to get a few sessions with a trainer so that I could learn how to use the weight machines - strength training is important during weight loss so that you don't lose muscle while you lose fat.
BUT, a gym isn't necessary. You can get some cardio in at home just by marching in place in front of the TV for 30 minutes or so. Over time you'll be able to march faster and for longer, and when the weather gets nice you can get outside for walks.
When you're ready, incorporate some strength training by doing body weight exercises. The straight-forward exercises you already know about are actually great - crunches, squats, lunges, pushups, etc. Do whatever modifications you need to with these when you get started, e.g. do the pushups against a wall or on the arm of a sofa, squat while holding onto the edge of a sturdy table or doorknob, etc.
ANY exercise you incorporate is going to reap benefits, and you'll be surprised how quickly you progress. Good luck!