The first couple of things you will want to do is work on getting pre-approved with a lender and finding a Realtor to work with. Ask around work to see if anyone had a realtor that they enjoyed working with, or go to a few open houses and talk with some of the agents until you find someone you can connect with.
The Realtor may have a couple of lenders they can recommend, but you will want to meet with someone early on in the process to get pre-approved. This will help you to understand exactly what you can afford, but it will also give you a stronger offer when the time is right.
Take some time to talk with one or two of the agents and sign a buyer's rep agreement. Make sure you understand if you are on the hook for any fees or if the seller is paying your fees. It is somewhat common for buyers to have to pay a processing fee of a couple of hundred dollars at settlement if they purchase a house, but otherwise your agent will probably get paid from the seller's commission.
Once you are working with an agent, he or she will walk you through the rest of the process, but basically you will set up some time to see 4 to 6 house. Usually within 2 or 3 trips out, you will narrow your search down to something that you like and it will be time to put an offer in.
After the offer, you start working closely with the loan officer to finalize the financing and will probably also have some things t the house, such as your home inspection.
Settlement in NC will probably take place at a title attorney's office where they will have you signing documents for about an hour. Then you will get the keys to your new home!