“I wish it would stop raining.”

It's a dark and rainy day. You're in the elevator with someone who you've met before, but you don't know very well. You want to make quick small talk to be polite, so you say:

I wish it would stop raining.

I wish (something) would (happen)

This phrase is used when you want something to happen, but you don't think it's very likely.

People often mix up "I wish..." and "I hope..."  The difference is in how realistic your wish is. For something that's not very likely, or is impossible, use "I wish..."

I wish I'd studied something a little more practical.

For something that hasn't happened yet, but might still happen, use "I hope..." For example, in the case of rain, you can say this before the rain starts:

I hope it doesn't rain.

This is OK because it's still possible that the rain won't start. After the rain starts, you can say:

I hope it stops raining soon.

stop (doing something)

Use this to express an action that stops:

Stop staring at me!

Don't use "stop to (do)" - that has the totally different meaning. It means to stop what you're doing so that you can do something else. For example:

We need to stop to get gas.

it (is) raining

When you talk about weather, use the word "it":

It's nice out today.

Has it stopped raining?

Have you heard that it's going to snow?