You can't actually change your address shown on a tax return if you've already filed it. However, if you requested an electronic direct deposit of your tax refund, then your mailing address shouldn't matter.
That said, to change or update your address independently of your tax return, you can file Form 8822 with the IRS. It's a simple one-page form with one page of instructions. You can fill it out by hand and file it by regular mail. Here is a courtesy link to that document:
Alternatively, you have some other choices, including calling the IRS by telephone (1-800-829-1040). These choices are outlined and explained at the following IRS.gov webpage:
There are similar procedures in place for your state department
of revenue, if applicable. Simply follow the basic process above (find
out if there is a dedicated form to file, or you can call them and
verbally tell them your new address).
Thank you for asking this question.