Before battle, the Rashidun army would send its elite squad of "Mubarizun" to challenge the opposition's generals and commanders. Now this was not a tactic that unique to the Rashidun, the army of the Prophet Muhammad also had these champions who would duel with the enemy and the Persians were doing this well before the birth of the Prophet.
The duels could either be one vs one or squad vs squad. For the most part, it was a no-holds barred fight to the death and in the case of squad battles, combatants would aim to defeat their opponent quickly in order to help out a struggling team-mate.
The champions of the Muslim army were picked on skill and duelling prowess. It was rare for the commander of an army duel for understandable reasons, with notable exceptions being Khalid ibn Al-Waleed and Abdullah ibn Al-Jarrah. Generally, the warriors who were exceptional at dueling would be placed into a unit (Mubarizun) and whichever warrior was feeling up for it on a particular day would step forth.
These were obviously not like the duel we saw in Troy, for example, where two individuals decided the outcome of the whole battle. The duels were for hyping up one's comrades and demoralizing the enemy.
Some interesting tidbits regarding duels of the Rashidun army:
Most warriors would be well-equipped with armor when fighting one v one. However, Dhiraar ibn Al-Aswad was famous was dueling topless and became known as "The Naked Champion".
There were instances of sabotage. On one occasion, the Sassanids tried to eliminate Khalid ibn Al-Waleed while he was engaged in a duel by sending a group of soldiers to kill him. Khalid is reported to use the Persian champion he was dueling as a shield long enough for backup to arrive.
The Rashiduns reportedly never lost a duel.