I want to enable user avatars in their profile and display the avatar with their posts. They need to enter the URL to their avatar.

What is the default directory for avatars. I don't have access to the website only the UBB.threads forum control panel.

Okay your question is not clear.
If you are going to enable avatars, default or offsite then all you need is control panel access.
Since you are not hosting custom avatars for them to upload.

Obviously, I don't know the proper steps to enable the user avatars. The Version is 7.5.5. Can you point me in the right direction? Sorry for my newbieness!

Sheese, figured it out. I always make everything difficult trying to out smart the system. Sorry.

No problemo.
Probably first item to enable would be:
Control Panel » Display Options [-] Topic Display Options
Enable Show User Avatars?

Second would be:
Control Panel » Site Permissions
Can specify a remote avatar
Can choose a stock avatars
Enter a 1 for each group allowed

Also the user may need to enable the avatar display in mystuff?edit preferences
to see others avatars.

Thank You.