You can do body weight exercises, absolutely. The problem is your own body weight will only take you so far. Of course, it depends on what your goals are if body weight will be enough.
If you want equipment, a great resistance band set and a set of handheld weights (please buy something more than two pounds. please. 5s, 10s, and 15s. please.) will get you going. You can also buy a barbell set if you're interested in doing a low weight/high rep workout... if you want heavy weight/low rep, it will get very expensive and also unless you have plenty of space to store them it's kind of a PITA. The bar I own was $20 and the plates were anywhere from $3-8 depending on the weight.
If you want to build serious strength, though... a gym is the way to do it. You don't need anything fancy or expensive. I don't know if you have them there, but here we have a lot of cheap gyms that are like $10/mo. You don't need a lot of cardio equipment or anything like that. You need access to barbells, dumbbells, a power rack or squat rack, and a bench. That's really all you need. And a lot of the cheap gyms have that and it's all good!
How to pick a gym:
http://www.nerdfitness.com/blog/2013/03/18/strength-training-101-finding-the-right-gym/
And what to do when you're in the gym:
http://www.amazon.com/Starting-Strength-3rd-Mark-Rippetoe/dp/0982522738/ref=dp_ob_title_bk
Another one:
http://www.amazon.com/The-New-Rules...tmm_pap_title_0?ie=UTF8&qid=1391701796&sr=8-1
If you don't want to buy a book (you have to sign up for it, you get everything in e-mail, then you can unsubscribe if you like, because you will get pretty frequent sales-y e-mails from him afterward if you don't):
http://stronglifts.com/stronglifts-5x5-beginner-strength-training-program/
Don't be scared of the gym. YouTube is full of resources on how to use the equipment. And part of picking a good gym, IMO, is picking one where the staff is awesome. I know if I'm at my gym and I wanted to ask how to do something, I could go ask one of the staff and they would help me. I also know if I'm at my gym, there are SO MANY guys I can just turn around and look for and say "oh, hey - can you help me do X?" and they will be happy to help out. When you're a regular, you get a feel for who is in there to do serious work and who knows what they're doing... who you can trust for help and won't lead you down a poor path.
Also barbell training just makes you feel like a badass. Fact.