When an account violates any of the rules in the Terms of Service or Acceptable Use Policy, it is suspended. There are various different types of suspension that will be covered here.
If your account is suspended and the reason includes the letters "zt" then the likelihood of getting your account back is slim. Only open a support ticket about this type of suspension if you believe it is in error (please note that we can check). Opening a ticket to ask to be unsuspended will get nowhere. You'll just be told what you've read here, and will waste our time in the process.
Some accounts are suspended for inactivity. This is when the account holder fails to log into the forums the required once every 31 days (posting is not required). You can unsuspend yourself from the account panel for this type of suspension; there is no need to open a support ticket. If you do, you will likely be told to do it yourself from the account panel anyway.
High Resource Usage
Again, this is a temporary suspension where an account is suspended for High Resource Usage. This means that the account has gone over the limits on resources imposed by the system, and the account has been subsequently suspended. You can unsuspend yourself from the account panel for this, but after the third suspension the system may require you to open a support ticket so staff are aware that you are being suspended so frequently. Always check if you can unsuspend yourself first.
First, login to the Account Panel with your email address and password.
Next, click "Hosting" in the header bar.
Then click "Click here to view suspension history and options".
You will then see a page like the one in the screenshot to the right. On there you should see an unsuspend button.