You've already received good advice; I'd only add/emphasize a couple of things:
-focus on being a leader. While there's nothing wrong with pitching in and getting your hands dirty if the situation demands it, your job is to stand back, maintain "situational awareness" (a fancy way of saying "knowing what's going on") and ensure that your plan is unfolding the way it should. Don't get sucked into the weeds, because you'll lose control.
-establish a chain of command right away. This will clarify in everyone's mind what the hierarchy is. You'll want at least a 2ic. Once you've done your initial estimate, you may decide you want to designate team leaders as subordinate commanders, if the task seems to lend itself to break down into logical sub-tasks.
-take the time to make a good plan. In small party tasks I've assessed, one of the more frequent failures is a leader who rushes through developing the plan in order to "get to it". Trouble is, without a plan that everyone understands, you can't really succeed. On the other hand, if you develop a good plan and communicate it to your subordinates so that each understands his/her part to play in the plan, then you'll find that the task will essentially execute itself. That leaves you free to trouble-shoot, react to changes and watch things like the passing of time.
-incidentally, that communication bit above is key. Even a sub-optimal plan can be made to work if everyone understands it. Even a perfect plan that isn't communicated well is going to quickly bog down. Don't launch into execution until you are confident everyone understands their job.
-ensure that everyone is kept busy with what's called "concurrent activity". That doesn't mean coming up with "make work" for people, though. Most small party tasks are specifically designed to keep about a section's worth of people busy doing something for a half-hour, give or take, with lots of simultaneous bits and pieces of work being done. If some people finish their part of the task early, don't leave them standing about; direct them to assist with other tasks still ongoing. Even if they're not really needed, it will show that you are aware of your resources and are managing them.
-finally, watch your time. Another common failing I've seen is a leader who takes the time to do a good time estimate, then completely ignores it and loses track of time (this is especially true for those who let themselves get sucked into the nitty-gritty of the task and lose situational awareness).
Hope this helps.