I know that overall scenario well, it is called hiking in two or three days of steady rain…
1) Others have covered tent erection and take down. I use a tarp. two stakes at the bottom end, one stake to pitch the pole, two stakes to pull it out. This works even in a wind. I want to note that yes, it will be wet.
2) I toss my pack under my tarp. I take care of other things: water, toilet duties, if it is cold, I get some smaller twigs, etc for a *small* fire under the tarp (even if they are soaked.) I throw a couple larger sticks under to use as poles for ventilation. Why a fire? Because, a heat source will change the humidity characteristics of the air significantly.
3) I crawl in and pull out my ground cloth. Opening this up about half way, I mop it off with a bandana, wringing it out as I go. I pull gear out of my pack next, laying out my pad, quilt, and all my dry gear. Then I strip and change into dry sleeping cloths, but leaving my dry sleeping socks off. Then I push out/mop/push out my ground cloth. I usually hang my pants and hiking shirt on my cloths line (already attached.) Then I prop up the lower end for cross ventilation. Then I am free to start my supper. This will add some heat inside and I use the wait time to dry out a few twigs by the stoves fire., carefully splitting them to get fine fire starters. Then I pour in my supper and set it aside to cook/cool. This takes about 1/2 hour, maybe 3/4 hour.
4) I peel back my ground cloth and lay out for a small fire. Maybe I have a few rocks thrown in, maybe it is mostly mineral soil, or maybe it is too wet to care. Then I start a small fire that requires almost constant feeding…like every 3-4 minutes. It is usually about 8″-12″ around. It produces some smoke, so I usually lay down when I do this. Usually, the tent acts as a tunnel and will blow most or all of the smoke out, though. Withing 5 minutes things start to dry. By the time supper is ready to eat, I am warm enough and the food is ready to eat. Raising the temp even degrees will really change the inside humidity of the air…things will dry easily, though not anything thoroughly.
5) It often is getting dark and under a tent/tarp it is worse, so after I eat and make my cocoa, I let the fire die out and sleep. Note that my rain jacket is handy for any midnight toilet runs.
6) Around dawn or something before light, I start making breakfast. I cuss for a minute ‘cuz it is still raining, I am slightly damp from retrieving the bear bag, feeling lazy and drink 3 cups of coffee. I change into my wet cloths, and pack up my dry gear/quilt and ground cloth (mopping as much water as I can.) I zap some water for the hike (I use a steripen) and empty my platy usually on the fire. Then I pack up everything except my tarp and pot. OK, time to bite the bullet…I crawl out and as fast as possible pull the tarp down and pack it into my pot, wringing/shaking as much water out of it as I can. I put this on top of my pack, I am ready to go. I kick the fire around to leave a fairly clean site, maybe grab a hand full or two of leaves/needles and cover it (stomping it down some.) I say good-bye and I am hiking.
Note that hanging a bear bag can be a trick. You need to pull all food for the evening, then hang it. In the morning, it means a quick trip to retrieve it. Yup, it always means getting out in the rain.
Small fires require constant attention. I often break twigs to stack around the fire to help them dry. Wet ground will protect the ground from ground-fires, so I don’t usually worry about it. It is near the corner of my tarp (propped up) so it cannot be too big, anyway.