I'll admit, it is slightly confusing when you are brand new, but from an accounts perspective, each Stack Exchange site has a unique account. There is no single account that can log you into any other Stack Exchange site.
So if find a Stack Exchange site you want to join, you need to create a new account on that site.
Then you'll be greeted by the standard signup page:
So if you previously created a Stack Exchange Login (which is different than a Stack Exchange Account), then you should click the "Login with Stack Exchange" button
Stack Exchange sites support OpenId, which effectively is method for a common login for multiple websites. So you need to click the specific login you want to use and provide the appropriate credentials.
If you use the same logon and credentials that you used on your other sites, your new account will be automatically associated with your existing accounts.
If you accidentally select a different login, your accounts won't be associated right away, but it is easily fixable by adding new logins to your account. The nice benefit is you can have multiple logins so in case you ever lose a specific login (for example you change your gmail address), you can always get into the site via a different login.
To help with the confusion, you have to remember 1 very key point, logins are not the same as accounts. You can have multiple logins associated with the same account so you can have multiple ways to access your account should you lose the credentials for one of your logins.