I accidentally uninstalled my Pokemon go app, and now I can't find the button to sign back into my google account. How do I get the button to show up?
If the account has not been unlinked from the device itself, you can download the app from the apple store / google play and it will present the account as an option to sign in (or it may automatically select it).
If you have changed the password on the account and the phone is unaware of the new password, or if the account has been deleted from the list of accounts for this device, go to the settings for your device and select the option to modify a google account or add a google account. Once the account is back in place and the password is correct, you'll be able to log in again.
If the account has been deleted (ie doesn't exist on google anymore), you can try to create a new google account with the same name and password and if successful pokemon go will pick up the account and you'll be back in business; if the account can't be re-created (somebody else has already used the name for example), you can tell niantic support what has happened, no guarantees they'll be able to help you but it's your only hope at that point.