The player issuing the challenge nominates one of their character models to issue the challenge. If they do not have a suitable model in the fight, a challenge cannot be issued. Similarly, if there are no characters in the enemy units, a challenge cannot be issued.
To issue a challenge, choose one of your characters in one of your units in the combat – this is the model that issues the challenge. Once one challenge has been made, further challenges cannot be issued in that combat.