How do you make a USB power adapter?
At its core, a USB power adapter or "wall wart" is a 5 V power supply.  They usually have a universal input able to handle AC power line voltages from 90 to 240 Vac (-ish), and an output current of at least 1 A.  All USB warts are switching supplies, but there is no reason to stick to that for a home project.

But

An AC-to-DC power converter of any kind is dangerous for a novice to attempt.  Without getting into the technical difficulties of designing a custom switching power supply transformer or even using an off-the-shelf linear transformer, powerline voltages are dangerous.  There is a reason that UL and other safety agencies have pages of rules covering wire insulation, printed circuit board trace widths and spacing, and transformer construction.

If you are intent on going forward, consider purchasing a small supply as a component and mounting it on the board.  These are available with pc pins for board mounting, plus full safety certifications.