well basically there are 3 different types of air traffic control places.
First you have the tower which is what you see at the airport next to the runway.
![[Image: 070803_airtraffic_hmed_10a.grid-6x2.jpg]](https://msnbcmedia4.msn.com/j/msnbc/Components/Photos/070803/070803_airtraffic_hmed_10a.grid-6x2.jpg)
You are up in the tower and you have a headset on and a radar screen in front of you with a map of the runways and few miles out. Aircraft are separated in a way that they arrive to an airport in increments. you can see this if you watch planes coming into land they are normally a few minutes behind each other. when your in the tower you are talking to each aircraft and giving them direction to slow down, speed up, descend or climb to a certain altitude to maintain the proper separation. Most of the time as a tower controller the planes are already separated and all you do is give them a clearance to land. You are also at the same time giving other pilots a clearance to take off. In the tower there are 3-4 different positions that you rotate in and out of after each break. The Local controller works landings and departures, The ground controller directs aircraft from the gate to the runway and then hands the aircraft off to the local controller, and the other two are clearance delivery and sometimes local assist.
The second type of air traffic control you can work is the approach control or some places have what they call Tracon.
![[Image: 1703245356_978fe6d924.jpg]](http://farm3.static.flickr.com/2088/1703245356_978fe6d924.jpg)
this is at the bottom of the control tower and if basically handles traffic that is say 30 miles out from the airport. so they get aircraft handed off from the enroute/center and then give them directions to maintain proper separation as they get closer to the airport. then they hand them off to the tower controller who proceeds to land them. they also take aircraft from the tower controller and separate them until the fly out of their airspace probably around 30miles from the airport then hand them off to the enroute/center controller. these people sit in a dark room and just monitor a radar scope while talking to the aircraft.
The last type is the enroute/center.
![[Image: traffic_f.jpg]](http://www.wired.com/images_blogs/thisdayintech/2010/01/traffic_f.jpg)
They handle aircraft while they are in between airports. Its much like the approach control or Tracon but they handle a much wider distance. The atmosphere is pretty much the same as they are sitting in a dark room monitoring a radar scope and talking to aircraft and you cannot see any aircraft.
I myself prefer the tower because you have a great view. The centers are darker and working traffic is much like a weird version of Tetris. You constantly have planes coming in and you need to make sure they get to the airport/runway with proper separation. Certain periods become very busy which is where controllers make their money because they need to be focused and on point. This is why you get such long and frequent breaks. Another downside to the center is that there are far fewer centers as they generally cover 3 to 4 states so your choices of where you want to work are reduced greatly.
So to answer you questions more directly you are giving commands to pilots verbally while monitoring a radar screen or visually looking at the plane on the ground. The problems you are solving is how to get planes in and out of the airport in the most efficient way while maintaining the proper separation and safety.