Many questions about gaining muscle

I do reformer pilates and jivamukti yoga too. Those help with good toning and strength.

I have recently met my weight goal. Despite wearing small sizes, I don't always "feel" so small. I still have small amounts of extra skin around the hips and my butt needs some toning. It's not terrible but it is a bit bothersome. I'd like to start building some muscle. I'm not looking to get abs or anything major. I'd just like to see some definition. My maintenance calories are at 1580. I have heard that you should be eating at a surplus to gain muscle. How much should I increase my calories? Do you need to eat at a surplus every day or just on the days that you would be doing weight training? Why exactly is there a need for a surplus when trying to gain muscle? Last but not least...when doing squats how many reps is suitable and how often during a weeks time should they be done to benefit from them?

For programs to use, the ones mentioned above are good.

What you could try and do with calories....is on days you workout, eat a surplus.
On days you don't, then eat at maintenance.
Try that for a couple weeks, and see how your body responds to the new workout and eating routine.
If you like it, then continue doing that.
If you think you need more energy (food), then on your off days, you can up your calories.

For your workouts, and squats.
Try to shoot for the 6 - 8 rep range, and the weight should be at a point where by reps 6, 7 and 8.....you are struggling to squeeze those reps out.....shoot for about 4 sets.

The programs listed above will include things like squats, deadlifts, bench press, chin/pull-ups......those will be a staple in your workouts, and for which ever muscle group you hit, one of those exercises should be included.
For example, if it is a leg day, then squats will be an exercise you do, and you can then include any other leg routines you wish.....like extensions, leg press, etc...

Make sure you are getting adequate protein daily, so you should be 0.8 - 1.0 gr / pound of body weight.

Regarding frequency, I would say it depends on how hard you hit them....
So for me, I will do legs today.....I will hammer them, so I will be up for legs next week......
But the standard rule of thumb for muscles is usually a 48 - 72 hr rest period.......
So if you were to do legs on Monday, then if you wanted, you could hit them again on Wednesday or Thursday.
But if you are hammering them, once a week should be fine.

Since we are discussing legs....
I am doing mine today as I mentioned.

So what I will be doing is this.
I will do 2 sets of warm ups....so this is a light weight ~135 lbs, maybe 6 - 8 reps.....
Just to get me going....these 2 sets do not count.
Then I will do my 4 sets, 6 - 8 rep range, with about 1 - 2 min rest between sets.
Weight will be:
Set 1: ~205
Set 2: 225
Set 3: 245
Set 4: 225

Then I will move onto calf raises, leg press, leg extensions.

If the back of your legs are points of interest for you, then include lunges.....man those things hit the back of the legs great.....

Check out the group stronglifts 5x5 for woman https://www.myfitnesspal.com/groups/home/4601-stronglifts-5x5-for-women, the ladies over there will answer all your questions and help you get started.

This.

Effective but simple program to follow