A fairly straightforward process, when on the invoice page, you have the ability to record a payment towards any UNPAID. PARTIAL, or PYMTPLAN status invoices. First off, you'll need to make sure your user access settings permit this feature. To check this, go to the left nav panel under Configure > User Access. From there, just make sure the "Make Payments" check box is ticked. If this is the first time configuring this option, you'll need to log out and log back in for the changes to take affect.
Once done, just go to the invoice page and select the "Accept Payment" button. If you don't see this button, make sure the invoice status isn't set to PAID.
When selecting to "Accept Payment", you'll be given the option to either choose a "Credit Card" or other offline payment types. If you have any custom payment types, they'll display under this drop down as well.
Here are some supplemental articles for questions you may have when accepting payments: