If it's okay with you, I'll just give an example of how I started back up after a long, long hiatus. Three times a week, every other day, then something different for pleasure at the weekend (swim, pilates, yoga, walking, run-walk, run. Or sleeping and a very long bath followed by at home stretching whilst watching TV, whatever works for you).
15-20 minute walk to the gym.
In gym, warmup on the rower - water bottle to your side, put your headphones in and get your music playing, rather than the piped stuff.
Set the resistance about 5-6 and go for a stroke rate of 28-32. No going mad on it and yanking hard with your arms, just concentrating on keeping a nice, steady, even motion with no discomfort and maintaining good posture and form for ten minutes. When you finish, drink some water and take a short time to get up, as depending upon your base level of fitness, you might feel a little wobbly. Shake your legs out a little as you get the cleaning spray and paper cloth, clean off the seat and handles and move on.
Next, go to the leg abductor (open) and adductor (close) machines. They'll be the ones that rarely have anybody on them.
Set the weight to minimum and the position of your legs to 'comfortable' (open/outside the pads and squeezing in or closed/inside the pads and opening out) using the handle to your right had side (lift and allow to move to the setting you want). Do a couple (opening or closing) to see how you feel - they could be ridiculously easy, so bring the weight to rest and use the pin to select the next plate. You need to feel like you're doing something but not that it takes all your effort to get it to move. A controlled rhythm works, say 1-2-3-4 out-2-3-4. Have a go at doing ten. Have some water. Do another ten. More water. Do another ten (or do multiples of eight - the last couple of a set should feel like you had to put some real effort it but not that they kill you). More water then use the handle to release the pads so you can step off without falling over. Clean the machine.
Swap to the other machine and do the same. You may well need to use a lighter weight on one movement compared to the other. Drink water, clean the machine, move on. I tend to go to the leg press next if it's a legs day.
Adjust the machine so that you have your feet comfortably flat against the plate, back well supported. Do the same trying the motion, then trying a weight. It's a good stretch for your hips as well. You can do it more slowly - don't try to go at warp speed and don't lock your knees out straight - you'll feel it in your butt most.
Depending upon how you feel now, you could do leg extension (it works on different muscles) or, as you've done 15 minutes with warmup, you could look at warming down. It's easy enough to go back onto the rower for another ten minutes. More water, shower if you do that at the gym, walk home, have a good meal with your choice of protein in it shortly after you get home.
The following day, you will likely have some sensations in your leg muscles. It'll be ok, they shouldn't be agony, just a little tender at most. It'll go by the next visit with the warmup and if you're feeling brave, a foam roller will help get to spots you didn't know you had in the meantime.
Next time, instead of concentrating upon your legs, you could do your back and arms - so you try lat pulldown, overhead row and bicep/tricep machines. Time after that, back to legs.
All the machines have instructions on them, so it's not hard to work out how to use them, and there should always be a member of staff around to ask questions, anyhow.
After a few visits, you might feel like you want to do more on the rower, try out the treadmill (NO leaping on it whilst it's moving, starting off at walking pace (3-5 kph) and ALWAYS fit the emergency stop cable by attaching it to your waistband) or another machine. Remember that nothing should hurt, especially not your knee - don't ever be embarrassed to say 'Actually, nah' and get off.
That start will help give you an idea of where you are strong, what muscles have been neglected and will be, despite what people may say (and completely put you off the idea because they can't conceive of anybody wanting to start something sustainably or wanting to avoid injury) absolutely great.
And then, once you are feeling the difference, you can mix it up some more, possibly increase what you do, change intensity or activity. But at the moment, you need to start. And we all know the hardest exercise of all is the putting your kit on in the first place.