A fight starts with surprise if one side doesn't notice the other approaching before combat begins. If neither side is sneaking, then combat begins normally.
If one party is sneaking prior to the start of combat, then the GM should compare the lowest stealth check value in that group to the passive perception of each creature on the opposing side. Any creatures that don't notice the enemy approaching are surprised. Combatants that are surprised skip their turn during the first round of combat, and can't use reactions before their first turn unless they succeed on a difficulty 20 Reflex save.
If both parties are sneaking, then this process should be repeated for each side. No combatants are surprised on the side that notices the threat first. On the other side, creatures that don't notice the other party are surprised.