Q: How do I get rid of an icloud account? I want to join my wife's account.

Are you sure?

you can use the family sharing to link them and that creates a shared Calendar, Photo Album and you can even share the purchases.

Family Sharing - Apple Support

and

Sharing purchased content with Family Sharing - Apple Support

If you still want to

Settings > iCloud

     Turn off your Find My iPhone

          All the way at the bottom sign out

Sign in with her account

No, the iCloud accounts are your own.

If you are going to change iCloud account, make sure you backup your account info.

Archive or make copies of your iCloud data

https://support.apple.com/en-us/HT204055

iCloud accounts are NOT intended to be shared. You're inviting headaches by doing so.