I'll be the advocate of the devil here and say, I disagree with those who've recommended long rest periods and long times between workouts. In fact, I suggest in a week or two you add in a 5 burpees with each set of squats.
Like some have mentioned, there will be a steep curve for you, which is a good thing. You're at a point where your body will learn very quickly what it needs to be doing, because it is not used to doing it all.
But, not only will it gain muscle memory and heal fairly quick as you push yourself, it will gain a relatively massive amount of strength and endurance. All that said, the best way to see improvement, especially right now, is hard and fast: high intensity.
Keep your rest periods to 60 seconds or less.
Time it if you must. Even if it takes you 30 seconds to do each squat: be doing the squat, not standing there thinking about how you should be doing it.
Your body is much more capable than you'd imagine. The harder you push it, the faster it will respond (mind you have proper nutrition, which I hope you do, being here and that you're getting enough sleep).
I can't stress enough how important eating healthy is.
But more than that, sleep. Sleep. Sleep. Sleep. Go to bed. Like I'm about to do. Go to bed, sleep longer than normal. Get that sleep. How many times must I say it? Your body will want it, your mind will thank you for it, sleep. Seven times.
If you have any sort of item that weighs 5-20#s that you can hold above your head with both hands, I'd recommend using that in about 2 weeks. Overhead squats are by far the best squat out there, in my opinion, and in others. But, don't take my word for it, research.