I want to start playing some Western/steel-style music on my acoustic but I'm not really sure where to start. I really enjoy the Civil War era sound, like the theme to Hell on Wheels or the band Brown Bird, etc. Any help or tips on how to get started? Thank you all very much in advance!
By "steel" I assume you're meaning "steel string" rather than like perhaps "lap steel"...

Hey, I like those Brown Bird folks... Nice stuff. Anyway....
Mostly what I'd call contemporary folk flatpicking. Most of what's being done on the guitar is alternating bass and syncopated rhythm strumming.
It's not the strict "boom-chicka-boom" type strumming you hear in bluegrass, but a little more bluesy.
Your main chore is to get the rhythm down.
Try listening to a lot of these contemporary "alternative country" types for some possible insights:
Jeffery Foucault
Kieran Kane
Steve Earl

If you look those guys up on YouTube they'll link you to many more.