You can handle that bit just as you always did. The battles really aree basically "set pieces" for the in combat mechanic of the game. If you want to graph your travels through the dungeon on paper, based on DM description, you still can.
If it is a small area/dungeon, you could potentially feasibly tile or draw the whole thing in full scale.
Some take a more fluid approach and "assume" the party to be mapping as they go but rely on the DM for actual reference in the parts they have seen.
All the above is largely in effect for dungeony crawls anyway.
Ok, that pretty much makes sense. Your players can map on paper and then encounters are set up on tiles or maps. I can see how that works.