We generally recommend resistance (weights) for strength-building, but some people are just afraid of weights or associate them with body-builders. Wrong, but whatever.
However, there are some exertions which can be useful upper body fitness-builders without weights. Four calisthenics in particular: Pushups, pullups, planks, and Burpees.
These are far from comprehensive, but they cover lots of the basic muscle groups, and proper pushups stress core too. There is a reason these are basics of military basic training.
Another good thing about them is that they can be modified until you can do the real thing. For examples, you can do "girl" pushups (on knees) until you can do real ones. You can do assisted pullups (with bands) until you can do real ones. Everybody can do straight-arm or elbow planks, but duration is the challenge. Aim for several minutes. Shoulder-touch planks are a cool variation. Burpees (with the pushups and jumps) are a great upper-body and whole body calisthenic.
How many? That depends on you. Generally speaking, for a middle-aged (45-75) guy or gal who avoids weights, I'd aim for 25-50 pullups assisted or not, 100 pushups (modified or unmodified), 3 or 4 30-45-second planks, and 50 Burpees. Not all in a row, but on the same day.
(For general fitness without weights, this can (should) be coupled with a day of lower-body body-weight workout (eg lunges, squats, step-ups, box jumps, etc) plus a couple of days of cardio. That all is good enough for casual or club tennis fitness, or for a long day hill hike.)
When life gets back to normal, then we can return to our usual routines. Or maybe just stick with these sorts of things.
