How do carrier-based planes find the ship after a mission ?

with a sextant and a compass they know ware the ship was and it's heading
so it was not hard to comput the heading to intersect ths ships heading......

Carrier-based pilots did not use sextants. They used a "plotting
board" and returned to the boat by dead reckoning.

If you look at WW II documentaries, you will see the carrier pilots
running to their planes carrying a flat object that looks sort of like
a notebook. That's a plotting board. It slides into a slot under the
instrument panel, and could be pulled out like a drawer when in use,
or pushed back in.

Well if the ship steered a constant heading and there
were no cross winds or currents

Not required. Pilots could easilys account for changes in the boat's
course, and for cross winds, provided both were known before takeoff.

If you know how to draw a simple wind triangle, try doing this for
yourself. Not as easy as with a plotting board, but it can be done.

vince norris