Getting your mail forwarded through USPS to another address when moving is easy.
All you need to do is go into your current post office or any post office and pickup a USPS change of address form.
This form should come in an envelope with some other advertisements and papers. Sometimes you can get the form off the counter and other times you might have to ask a postal employee for the change of address form.
Once you get the USPS change of address form you then just fill it out and then mail it in the provided envelope.
Then the USPS will take care of everything regarding your mail forwarding after they receive the form in the mail.