You don't have to go to the gym to exercise. Plenty of bodyweight exercise (like push-ups, L-sits, planks, burpees, etc) can be done at home without any equipment.
Investing in a little bit of equipment, like barbells or maybe a pull-up bar, can let you do even more exercise at home.
While I could Google this, I often prefer asking people I 'know' even as tangentially as via HN comments: any suggestions for resources about this? I'd like to exercise more, and I have an entire room available, but I'm not sure where to start. I have the one-handed weight thingies, for one, but a pull-up bar is not an option. I heard one of those ball thingies with a handle is useful?
https://darebee.com is another good site. They have lots of videos explaining various exercises. Just make sure you start with the entry-level exercises to slowly build up your strength.
I'd even recommend to not worry so much about timing your workouts as this causes too much stress, just focus on the exercises themselves in the beginning to make sure you do them properly.
This app may be useful to you. I've used it for about 6 months and have been pretty happy with it. You can customize what equipment you have available so that it builds you a workout based on that. On the other side, you can look at what equipment it lists and determine what you want to buy.
Investing in a little bit of equipment, like barbells or maybe a pull-up bar, can let you do even more exercise at home.