That's going to depend on your local laws. I'm presuming you're talking about putting up a marker on a public thoroughfare or maybe on the sidewalk in town.
In Texas, you'd normally start with the local county historical commission, which can assist and review marker applications. The application is then submitted through the county commission to the state, which does its own review and drafts the actual text that appears on the marker. Local folks also need to make arrangements to pay for the actual manufacture and installation of the marker, which could run to several thousand dollars, depending on the type of marker wanted. If there's private property involved, you'll need to secure the owner's formal agreement, as well. It can be a long process, and local personalities and politics can play a role in that.
I don't know the process in South Carolina, but it's tightened up a lot in Texas over the years, and having very reliable scholarship behind any application is a must. That will be particularly important with a contentious subject like Sherman, where there are all sorts of traditions and legends told about him that may or may not be accurate.
Anyway, your first step is to get with the local historical groups, especially those that have an official affiliation (like county historical commissions here in Texas), and start with them.
Here's a link to information on how to prepare a marker application in Texas; although the specific details will be different in South Carolina, I think you'll probably need to deal with similar requirements there.
Bringing the