Line your pack with a garbage bag. Wear a tarp /poncho The poncho will cover your pack, too. Put your tarp/tent where you can get at it first out of the pack. Keep it outside the liner.
Set your shelter, get inside, replace whatever clothes need replacing. For the time being put your wet things in a plastic bag or stuff sack. My wife and I have walked in rain for 3 days straight and slept warm and dry. I like tents that you can put up the fly, crawl underneath and clip up the inner. Tarps are quick and easy for the rain. ALWAYS keep your sleeping gear and a set of sleep wear dry. If you have to put damp clothes back on in the morning, just get moving and you'll warm up, especially if you use a base layer of Merino wool. Fleece seems to work fine for me damp, also. I don't expect perfect comfort levels in wilderness, just tolerable ones. Adventure comes in adversity.
I do carry a mesh bag to tie outside my pack for things to dry in as I walk if the rain has stopped the next day.