I’m lucky to have the privilage of hunting about a 1/2 mile section of a small river in southeast Kansas. Being the only one that has permission to hunt this property I am able to put up hang on stands before the season and leave them for the duration. Hunting from treestands has been very successful for me, but know it would not work quite as well on public property.
Hang on tree stands work just fine on public land, but if you live in a state where they can't be left overnight you just need something like a Lone Wolf, XOP, or Muddy stand and sticks that are light enough to carry around with you. It's a little more work, but it offers a great benefit too in that it helps make sure you don't over hunt a particular spot or stay in a particular tree when you know you need to be 50 yds from there in order to have a shot.
In short, there's really not much that you need to do differently than you did with a compound, but you need to make sure that however you hunt you practice shooting from your stand, blind, etc. Depending on how far you were comfortable with shooting an animal with the compound, you may need to work to get a little closer than you're used to.
One small thing you probably want to look into is a way to keep your arrow on your bow without having to hold it in your hand, especially if it gets cold where you live. There are commercially available self adhesive products that stick onto a bow, and plenty of DIY solutions involving rubber bands and such that will release when you draw.
You can adjust things like brace height, arrow weight, string silencers, etc to get a really quiet bow, and you'll probably find more followup shots present themselves than when you hunted with a compound.
Other than that, it's still hold still, play the wind, draw when they can't see you, and aim small so you miss small.