HIIT is an old, popular technique; it's basically intervals of intense cardio separated by rest. For an introduction, see Couch-to-5K or the Zombies Run training app. Bodyweight exercises can be done anywhere. One reasonable introduction is You are Your Own Gym, but there are others.
If you raise your exercise intensity high enough to force your body to adapt, you can do a lot in 20 to 30 minutes several times a week without a health club membership. I'm not saying this is optimal-I'm not at all an expert—but it's certainly better than nothing, and I generally see far better gains doing this than when I do long, lower-intensity exercise.