This assumes you and your teammate already have a Challonge account!
Select 'Go to registration'

Enter your team's name, then select 'register'

Enter your name and that of your teammate.

Your team should now be registered!

In the bracket tab, select 'View my team'

Enter your teammate's Challonge username or e-mail, then select 'Add team member'

Your teammate should now receive an invite link to join the team.

Accept the invitation.

You're all set!