Half Dome
That is the way of it: pull yourself up a ways and rest a while. Below you can see people sitting around trying to decide if they want to climb the dome cables. You can see how everything slopes away here, so don't fall. The people down there gives you the angle of this picture: downward. You can see that the girl here has gloves on, and is using the standard technique for getting up the cables. Use both cables whenever you can.
On the Cables
The Hike to Climb Half Dome The cable route is mostly hard work going up. You pull yourself up, a lot of it with your arms, and then you have to rest for a while. A real traffic jam can form with people climbing at different speeds going up, and others coming down. Be safe.An unobstructed view of the cable route, with Clouds Rest and Quarter Domes in the background.
If you are really worried about the climb, bring a climbing harness, four carabiners and two sewn loops of webbing (REI and others have them ready made). Attach the loops to you harness with two carabiners (or use only one), and clip the loops to the cable with the other two carabiners. When you come to a pole, clip around the pole one at a time and continue on. You could not be much safer than that, but still, rely on your grip and smart climbing.