I went through basic about 30 (yikes!) years ago. It might be longer or shorter now, but mine was about 12 weeks long. It was in FL but they only have Navy bootcamp for women now in Chicago, I believe. Guys can go there or San Diego (unless it's been changed).
A typical day is: you get up at the crack of dawn, 5-ish. You have morning chow, then PT. You have classes all day, classes in stuff like seamanship. You might go through a little bit of training for biological/chemical warfare. I remember we had to go into a room with gas masks on and remove them after tear gas was sprayed into the room. You get a day on the range where you will get a chance to shoot a rifle (can't remember which kind, i.e, 22 or whatever, nothing like an AK-47) and if I remember correctly, also a handgun.
You have a weekly inspection of barracks and they teach you how to fold your clothes a certain way, the premise being that if you are on a ship or sub, you have very limited amount of space available to you. You have weekly uniform inspections. You practice how to march in formation. Lights out about 9 or 10. You also have "guard duty" where you rotate roaming the halls of the barracks. You must stay awake for your 2 hour shift.
And yes, you must pass a swimming test. I'm not a strong swimmer but managed to pass. Get a little practice in and you'll do fine, I'm sure. If I remember right, we had to jump off the diving board, stay afloat for a certain amount of minutes and be able to swim x number of yards. Google it, you'll probably be able to find the specifics.
I'll tell you one thing someone told me that helped me get through it: It's all a head game. They want to know who can cut and who can't. Do what you need to do, do your best and you'll make it.