What's a good procedure for cutting these 2 tall trees down? A neighbor and I will do it.?

Those are Arborvitaes. The limbs are small enough to cut with a good quality pruning shears.

Place a large piece of plywood on the carport roofs so your weight will be distributed over a large area. Prune the limbs off and toss them down. Then cut the trunks and toss them down. Then cut the trunks off even with the ground.

Cut the top half on the roof, then cut the second half at the base.

Maybe even cut the bottom half into a couple or three sections.

to be careful that those trees dont fall on you or any of your neighbors when youre cutting it down