First off, don't even think of attempting this if its raining or thunderstorms are nearby. Not only will water make the rock slick, but the prominence and the metal cables make people on the route prime targets for lighting strikes.

You are going to want to wear grippy shoes because of the slick granite and gloves to protect your hands.

What you are going to want to do to prevent a catastrophic fall is to clip yourself in to the cables. The minimum equipment for that is a rock climbing harness and a via ferrata setup. A rock climbing helmet would also be a good idea.

As you go up the cables, you will have one caribiner connected to the cable at all times. When you get to a post, clip the other caribiner onto the cable on the other side of the post, before removing the first. Like this.

[![enter image description here][1]][1]

If you were to fall, the caribiner would slide until it caught on the post. 

With that said, you **DO NOT** want to fall, because of the risk of hitting some one else and knocking them down, potentially causing them to fall. The odds are very few people are going to be clipped in.

Also, there is traffic going up and down at the same time so be mindful for other people.

Making certain that you water bottles are secured inside your pack so that they can't fall out and hid someone else is also a good idea.

Getting an early start will give you more time and allow you to take it slowly.

Finally, [permits are required][2], so definately plan ahead and get one, as the penalty for not having one is [rather steep][3].


  [1]: https://i.sstatic.net/gzuC4.png
  [2]: https://www.nps.gov/yose/planyourvisit/hdpermits.htm
  [3]: http://latimesblogs.latimes.com/outposts/2010/02/yosemite-half-dome-permits.html