League of Legends - How can I improve my last hitting skill?

Hop into a custom and practice last-hitting. I guarantee that you could be doing better.

Start without items and head to midlane. You can get a max of 114 CS from lane by 10 minutes. Challenge yourself to get up to 100 without any distractions. Go on. Try it.

Not so easy was it?

Now throw in a bot and see if you can juggle harassing, last-hitting, and not dying. Before you know it, you'll be seeing real results on how to outfarm your opponent in game, as well as get more comfortable with the damage output of your champ.

Also:

You can do this entirely with no items, with a full team of bots against you and choose a lane with two bots against you to mimic the pressure an actual opponent will apply. 

Also if you have free time you can make a custom game called "1v1". People will join pretty quick and you can learn a lot by playing against a variety of people who will have different strategies.