I've seen plenty of jokes about people and/or their pets falling out of shape during their time at home, and while I have nothing to say about the latter as my experience with pets has always been with indoor varieties, the former is just silly. Gyms in their modern sense didn't exist for most of human history, and yet studies keep showing how issues related to inactivity have grown more common in modern times despite them.
In other words, during the time when gyms have existed, people have been in increasingly worse shape. I'm not saying that they're all scams; I happen to know a personal trainer who does care about providing quality service to clients; but I would say that they are unnecessary for most people without special needs. All the equipment I use is a floor, a wall, a door-mounted pull up bar (similar to this), a simple towel, a few novels I don't care about (anything that can bear about half of your bodyweight safely and creates about six to twelve inches [15 to 30 cm] of elevation difference is sufficient), and occasionally a doorframe or table. For those who like working with external weights instead of calisthenics, I'm sure you can find furniture or other items (bottles of water, sacks of wood or stones, boxes of tiles, etc.) to improvise with.
In order to help people stay active without needing to leave their homes during the current pandemic, here are a few resources for information about fitness that I've used and recommend:
1. Convict Conditioning
This book played a big part in helping me find direction with improving my body, and I've written a review on it. As I said back then, I wouldn't read much into the anecdotes, and some of the instructions and progression targets on the high end of the scale are unreasonable, but the vast majority of it is great. Treat the notes on form for the last one or two steps of each progression more as idealized goals than practical (since it's almost impossible to do one-arm push ups with your feet together without any out-of-plane shifting or to do pistol squats without any rounding of the lower back due to simple physics of leverage) and use the "Intermediate" targets instead of the "Elite" targets for the final step in each progression, and it can serve as everything you need to get in shape. It may seem silly to start off progressions with some of the very basic exercises like push ups against a wall, but it actually does help in developing a feel for the motion in a low-load scenario in order to instill habits of good form.
2. Explosive Calisthenics
I skipped over the sequel to Convict Conditioning since the previews I saw didn't show much of interest to me in there (the next reference is what I suggest for stretching), but this third volume of Paul Wade's work is another good one. I'd still suggest starting with Convict Conditioning in order to build a solid foundation, but once you've gotten up to step five in its progressions, you can start mixing in some of these exercises to build more power and speed. However, I wouldn't recommend doing more than jumps, explosive push ups, and maybe kips until the pandemic is under control. Explosive movements generate far more force than slower ones (the rule of thumb for a bar meant for explosive lifts is to rate it for 1/10 the static weight it's designed for), so a structure safe for pull ups won't necessarily be safe for muscle ups, and front/back flips require ample clear space to do safely. Many health care systems are near or exceeding critical capacities already, so be smart about not putting more of a strain on their resources.
3. Stretching Your Boundaries
Whether you want to stretch as part of a post-workout cooldown or just want to do some yoga, Al Kavadlo has you covered here. This book doesn't have every type of stretch imaginable, obviously, and I personally prefer the structured progressions of Wade's books to Kavadlo's looser approach of clustering movements into related families, but I think the latter works better for a book on flexibility. For what it's worth, Kavadlo also has a less abrasive tone, coming off more like someone giving recommendations to a buddy as opposed to Wade's style of shouting out what he thinks is best and decrying alternatives in a hyperbolic way. I don't have a whole lot more to say about this one. Stretching is relaxing, invigorating, and when used well, it improves your body's resistance to suffering injuries.
4. 12 Minute Athlete
This was the site that turned me on to combining high intensity interval training (HIIT) with calisthenics, and it was also a huge influence on my belief that effective exercise doesn't have to take more than ten or twenty minutes out of my day. It's also where I picked up the format for my twelve minute HIIT AMRAP routines and why I got into the habit of doing 100 burpees as a monthly challenge. I haven't looked at it much lately (getting the URL for the link above was my first time visiting it several months), but assuming Krista Stryker hasn't done anything to purge old information from her site, it should still be a great resource with a huge backlog of workout routines. She does make more use of equipment than I do (mostly kettlebells, jump ropes, and punching bags, from what I recall), but there's plenty on her site that doesn't need any equipment, and I think she even has some specifically apartment-friendly routines, for those who want to avoid jumping around out of respect for neighbors below them.
There's more that I could say, but I'm going to stop there for two reasons: the above four resources cover everything that I'd consider essential for exercise (there's more to fitness than just exercise, but matters of diet and lifestyle are beyond the scope of this post), and because of that, providing more would risk inducing analysis-paralysis without adding significant value. You're always welcome to say something in the comments if you want to hear more, dear hypothetical reader, but pending that, it's more important to start doing something useful than to put it off until you find the perfect thing for you.
Now, there are also elements of discipline, honesty, humility, and reflection that are crucial for building good workout habits, and on those fronts, I can't say much. I've always been capable of driving myself hard, willing to wound my ego by admitting I'm not the best, and more concerned with doing what I think is important than with impressing others. If you need more help with that, try to recruit people to hold you accountable. That can be someone else who you're locked down with, a friend that you're in contact with regularly, or the oft-anonymous judgment of the Internet (if you post stuff on social media outlets, don't be discouraged when you almost inevitably get comments about how much better someone else is or asking why you're inflicting such misery on yourself).
Otherwise, stop making excuses and get to work. Even a bare strip of floor can be all the gym you need, if you apply yourself to it.