How to deal with rain?

Without knowing where you live, it is difficult to give a good answer.

If you're just interesting in grinding dust/candy, and not that bothered about shinies or IV/level hunting, then the Go+ (or Gotcha) is a good option. Your phone can remain safely dry in your pocket.

Another option is a clear plastic bag. You can tap/swipe the screen through the bag with some loss of precision, or get one large enough that you can put your other hand in. You'll get some odd looks from strangers, but that's par for the course as a Pokemon Go player. :)

Skywalkered answered pretty much perfectly, but I'd like to elaborate that good quality ziplock plastic bags are especially good for protecting your phone from the rain because they keep the moisture out well. Moisture between the bag and the phone will make most touch screens completely unusable.

I've done something to the effect of having the umbrella between my arm and the side of my body, trapping it in place with the force of my arm or putting my hand in the strap and resting it on my shoulder to keep me out of the rain, and then bagging my phone in something like a sandwich bag to keep the rain off the screen.

It makes catching a little harder, but you adjust after a bit.

A big plastic bag where you can put your phone AND your hand (big enough to go to your wrist)
I tried that for a community day.

Ziploc plastic bags actually work, but I suggest getting a waterproof phone case if you have the money. It's a good investment for not just PoGo, but it protects your phone pretty well. Also, a lot of new phones are water resistant.

Why no simply find place with few stops and lots spawn, like shopping center? Unless you live in rural area, is the best way to grind. Lure some stops( usually they already lured that kind of places). The only disadvantage is, that you wont do progress in hatching eggs and finding new quest, but lots mons to catch( with double stardust bonus) and potentially shinies with acess to balls and berries from stops around you.

Buy one of these

What works best for me is a backpack and an umbrella... I take the umbrella’s um “shaft” and place it thru the handle on top of the backpack so the umm “shaft” is between my back and the backpack and place the grip in my back pocket and snug up the straps on the backpack... that pretty much secures the umbrella from moving and allowing me to play with both hands ... a plastic bag for my charger and I’m all set.... personally I have used both a Pokémon go plus and a gotcha go during events on my Alt account and the results weren’t extremely different.. I have stoped using them and prefer manually catching...

This