How to access my PS3 with the new account?

No needs to logout your current account. All you need to do is just add a new user profile.
- Push the 'PlayStation' button on your Controller to back to the Main Menu.

- Move your cursor to the left corner of the Main Menu. Then select ‘User’ to ‘Create New User’.

- Create a user name you want, like User 2, then click ‘OK’.

- Now you are prompted to Main Menu. Just select the user name (User 2) you created above then push ‘O’ button on your controller.

- Choose ‘Yes’ and ‘Enter’ to the next.

- Now you will be redirected to PlayStation Network option. Please click the icon below to Sign Up.

- Then you will asked to choose a user to sign in. Please select ‘Use an Existing Account’ and click ‘Enter’.

- Enter the new account (Email and Password), then click ‘Save Password’ TO ‘Continue’ to the next.

- Then you will required to ‘Processed to PlayStation Store’. Please select ‘X Back’ to the next.