There are few feelings worse than hiking deep into an area that should be pristine and finding garbage. What are some steps that I could take to help prevent or lessen this?
Make certain that you are part of the solution and not the problem, never leave any of your own garbage behind.
As people are less likely to litter a clean area, remove as much of other people's trash as you can.
Document and report violators to the authorities.
Honestly, the best way to discourage people from littering is to be vocal about it. People are less comfortable leaving their trash lying around if someone voices their disapproval. And less likely to do it again in the future if they've been chastised once in the past.
Rhetorical questions like, "Hey, what are you doing? Show show some respect would ya?" tend to make people rethink their careless behaviour.
I'm one of those types who'll shout out at people I catch dropping trash on the ground, "Oh come on! Pick that back up!" they usually apologize awkwardly and quickly pick their stuff up off the ground, shove it in their pocket and shuffle off doing their best to avoid eye contact. I also take the time to clean up other peoples trash that I find on the trail, mumbling and grumbling about how inconsiderate people are while I do it, making sure people can hear me. These things tend to stick in people's mind I've discovered, they're way more conscious of their actions if they've had at least one experience with someone who's ornery about litter.