what exercises should i do

Find an established program with exercises for your entire body. Stronglifts and Strong Curves are popular ones around here.
There's also a thread - "which lifting program is right for you" that discusses many others.

ETA- sorry, didn't see the part about not lifting weights. There are some body weight programs discussed on the other thread. There may be some resistance bands options as well. Aside from that, you're kind of limited not using weights for muscle gains.

Hi Jody,

If you're trying to build muscle, you really need resistance exercises like lifting weights, but you don't need to do "Weight Lifting". Let's call it something else. If you are worried that weight lifting will make you 'bulky' don't worry, women's body's naturally fight against this and in any case it takes lots of time to build muscle so even though you might be doing "Strength" exercises, you won't 'get huge' overnight.

While you don't have weights, you could get yourself a gallon (4L) milk jug filled with water and do Goblet Squats, Overhead Presses, and Bent Over Rows, a One-Legged Romanian Deadlift with your milk jugs and Push-Ups. Look up some videos of these and check a few to make sure you understand the right form and especially how to position your back.

To make sure you are making progress, write down your starting program and increase repetitions or sets each week. That way you'll be able to look back and see how much you can lift now compared to 6 weeks ago etc. If you don't have time or don't want to, splitting these exercises up into different days works well, do three of them on Monday, then the other three on Wednesday, then do Mondays workout on Friday, take two days off on the weekend, then do Wednesdays workout on Monday, just keep going alternating workouts and taking a day off between them and two days off once per week.