How can I join trust back. I lied to my girl about not talking to other girls but I don't want to lose her I really love her we been together for a year now. And I need to know what can I do to gain her trust back

Regaining trust takes time, determination and patience.

SHould I give her space if I should for how long?

For as long as she needs it. Has she asked you for space? How old are both of you?
She is mad because you talk to girls? Have you cheated before or something?

17 & no I she never asked for space & I never cheated

So she thinks you should not talk to other girls. Are you flirting with them?

No but she won't believe me that I won't stop

Why would you tell her you will not talk to other girls? That is ridiculous! Is she so insecure she does not want you to talk to girls?

She don't want me talking no other girl. I know I ed up big time about the lies I made I just need to get her back. But its hard I try not to argue with her but all of a sudden an argument just appears. I try my best not to make mistakes its like I do a lot but she don't. When she's mad I try my best to make her happy. When I'm sad she doesn't take that much effort. She get mad at me when I get mad at her when she's doing wrong

Why would you want to stay in this relationship? I know you say you love her but you don't sound happy

But what if she is going to keep bringing the fact that I lied every time what should I do should I just give her space or what?

Just leave her alone. It is unreasonable for someone to tell you that you can't talk to girls. If she wants to be that foolish, leave her alone. If she says she wants to break up, let her. This girl is controlling you.

Its all my fault I've been insecure all the time annoying her trying to make sure things are okay but when she get mad at me I just keep calling her trying to make sure she fine. Im showing her that I care. She keep saying I need to grow up.

So does she, if she wants to tell you you can't talk to girls.
It sounds like there are problems in this relationship. Maybe it is time for it to end.
How long have you two been dating?

1 year & 1 Month

This relationship sounds pretty stressful for both of you. Maybe you need a break from each other.