How does it locate earth to .3 accuracy while they’re both moving ?

Voyager is so far away that from its perspective, earth isn't moving. There is also no force acting on voyager. So practically speaking, compared to the distance between them and the 0.3° beam width, both are hanging pretty still.

It does have an AACS system, which is tracking the sun and a bright star (Canopus) to orient itself earlier in the mission.

A quick search indicates it is still doing about 1 puff per hour to keep pointing the right way. The biggest problem seems to be that the lines for those puffs are clogging.