I use side-based initiative, and when it's the players' turn you can all go in any order. For your action, describe what you're doing and include any necessary rolls, including damage (ie Longsword attack, 1d20+3, 1d8+1). If you cast a spell that requires a save, include the DC in the roll description (ie Poison Spray CON save vs DC 14, 1d12).
You can also describe your bonus actions and reactions if your character has any. I like seeing them written in your IC post, but I don't mind if you have to state OOC what you're doing.
I don't intend to use a battle map, just theater of the mind. I do try to describe ranges, however, as sometimes those become important. Your movement on the battlefield should be reasonable, and you can move, act, and move again if it fits within your character's Speed. If you wish to do something that might require a roll during your movement, like leaping over crates or parkour off the wall, add an Acrobatics or Athletics check. I may not actually use it based on what I think you're trying to do, but in that case we just ignore the roll.
Example:
D'artagnan rolled over the back of the fallen hobgoblin and ran to support his friends. Finding an opening, he thrust his rapier at the bugbear, then quickly tumbled backward out of the expected counterattack.
OOC:
Bonus action, Disengage
