Saving advice

I just had my first baby in December and am currently living with my mom and I absolutely hate it here and her. I am however stuck here until I find a place so I don’t complain and I stick to myself. I go back to work at the end of this month and just want some advice on saving and how much do you guys think I should save up before I move out? Ill only make about 500 every 2 weeks considering I lll be goin back part time instead of full time. Any advice on saving money would be greatly appreciated!