So in Dungeon World, there doesn't seem to be any stat for initiative or any structure to the sequence of moves that people can make. Is the game intended to be simply played "round robin", or do some people tend to make entire series of moves in a row, or what? I'm coming from games like D&D and Pathfinder, so the absence to a structure to the combat turn order is both refreshing and confusing.
It's up to the GM to direct turns in combat by switching between characters, often by asking "What do you do?"
The easiest question to use is "What do you do?" Whenever you make a move, end with "What do you do?" You don't even have to ask the person you made the move against. Take that chance to shift the focus elsewhere: "Rath's spell is torn apart with a flick of the mage's wand. Finnegan, that spell was aiding you. What are you doing now that it's gone?"
The Example of Play chapter also demonstrates these transitions.
I suspect the same character making multiple moves in a row is boring and goes against the fill the characters' lives with adventure agenda.
Make the game more narrative!
Even though you have turns, don't forget that in a round of combat all actions are contemporaneous. (In some rule-sets the terms "turn" and "round" have their meaning swapped... by the way the idea is the same...)
In a round robin approach you can just collect all players' actions in a turn of combat and just explain what happens accordingly to what you (the GM) decide for NPCs/Environment to happen.
Furthermore, players must always describe their in-game actions in order for a move to be triggered; for example, it's not permitted to say merely
I perform Hack and Slash move on target Xavier.
but maybe something like
I attack Xavier with my broadsword paying attention to what Lucy does.
Acting like this, the player can express his will to interact with Lucy the following turn.
It's enough to keep in mind that you are roleplaying and not playing a video game.
I try to imagine the narrative of combat as being a bit like a soccer game. The spotlight is passed back and forth and sometimes intercepted. You want to make sure that everyone gets a chance, but remember, the GM's mandate is to always ask "What do you do?" and to be curious about the situation. Think about who each action might affect and ask them how they respond. Luckily, you only have half as many active members of a battle to think about - the monsters only go when the PCs look to you as if to say "well, what does the Ogre do now?" or when moves indicate they get to do something. The players will pick this rhythm up and start jumping in to have their say, too.