Step 1: Check here:
If there is a spike in reports it usually means there is a problem with the servers.
Step 2: Wait
Usually the servers will come back up soon.
How to prepare for if the servers go down.
Step 1: Load up the app
Load Pokemon Go as you normally would.
Step 2: Linking another account
Press the Pokeball, then settings in the top right.
Scroll down a little bit, and you’ll see
Google NOT LINKED
Facebook NOT LINKED.
Step 3: Choose your account
Decide if you want to link it to a google or facebook account. It will need to be a secure account. If you have already got an account registered to one of these accounts, you will not be able to connect it to that one. If you need to make a new Google account, you can do that by signing out and signing in with google, assuming you already have 2 or more accounts. If you have one, then some instructions are here https://support.google.com/googleplay/answer/2521798?hl=en-GB .
Then restart the app. Log back in to your account as you normally would, if you signed out and then press google and link.
I’m not sure how linking to facebook works, but https://pokemongolive.com/en/post/accountlinking/ implies it should be self-explanatory.