Ice screws are the most important piece of equipment in ice climbing. Ice screws secure you to the ice. After inserting an ice screw into the ice, the rope is looped through it so that you don't fall all the way to the bottom.
Ice screws can vary in length but the 6-7 inch variety are the best to buy because they are more secure in the ice and don't get pulled out as easy. Ice screws are hollow so that as they go into the ice, the ice gets pushed out behind it so it stays consistent as you screw it in. Most ice screws have a single, long tooth that spirals around the shaft so that it screws into the ice. At the top of an ice screw, there is usually a protrusion that you attach the carabiner to. The carabiner is then attached to a sling or runner (same thing), this relieves tension from the screw itself so that it pulls out of the ice less easily. On the other end of the runner, another carabiner is attached, this is the carabiner that you run the rope through.
Inserting an ice screw is very difficult on a vertical slope. You need first to secure your feet so that your can move your hands about without falling. You will also need to put your axes/hammers into the ice and make sure that the leashes are around your wrists (so that you don't lose your tools). The ice screw itself has teeth on the bottom, so you should put these on the ice. You can tap it with an ice hammer, to get it started, or just screw it in, it's entirely up to you. Once started, it can be difficult to get in. If this happens, as it should, then you can take one your tools out of the ice and use it as a screwdriver to get the screw in the ice. If you hit rock before your screw is all the way in, you need to take your runner and remove it from the head of the screw.Use a hitch knot to tie the runner to the shaft of the ice screw, this relieves tension from the screw. Once the screw is in place and the runner is in place as well, it's time to put the rope through. The carabiner at the end of the runner is where the rope should go through, but you need to make sure the rope isn't twisted around the carabiner. If it is then it may pop out of the carabiner and you fall much further.
Once all this is done, you're ready to start climbing again. Have fun!