good eye tinner.
and just like shangle said, just because the gutter is pitched the other way, doesnt mean in heavy rain that lots of water isnt going that direction.
so in this order:
cut and cap gutter. either put hole so it drains to the lower section, or let it run to the right.
remove shingles in that area.
replace rotted wood
install waterproof membrane
install valley metal, allowing it to slightly overhang the end of the valley.
install new shingles, making sure to take care to properly step flash where needed (against walls and that fascia where it meets the roof line.
relax and drink beer.
the final step is the most important, and must be followed or none of it matters. (the beer part, not the shingles)