I just adopted a cat from the street, what should I expect?

Hey! So since my beautiful dog passed away, a cat keeps coming to the garden… Today my family decided we will keep it! My dad did all the medical stuff and she will be with us but outside for now since its summer. I’ve never had a cat in my life and it seems so strange…

I want to pet her but she is like so cool haha she wants her space? She just lays down and just looks away… She is almost 2 years old by the way. I’m just afraid to approach her..
She is a tabby cat… What can I do to make her like me?