you have to have 2 different terraria windows opened.
You need to know what your IP is and to find that out click the start button in the bottom left and search for "CMD" when you find it open it up and type in "configureIP"
look for your IP in the list of words that will show up it will be a number like 1.23.456.563
Now open terraria 2 times. on one of the widows you open go to multiplayer then start server, your charector, then the world
Now on your second terraria window go to multiplayer, join server, then type in the ip you got from CMD.
now for your brother to join that all he has to do is go to join server then type the IP in.
this will only work if you too are sharing a main IP. if your brother uses a different IP you need to download Hamachi.
and to start a server from there just open it and click create server. it will ask you for a server name and password. now isntead of the IP you got from CMD use the IP it says next to your username. you will still need the 2 terraria windows open.
You will also have to add a port to your router. with the IP you got from CMD copy that and paste is to the URL bar in the internet. if you use lynksys it will bring to you your router home page. click on the gaming tab at the top. there should be a list of ports on your router. in one of the ports name it "Terraria" i'm not exactly sure about the rest i watched a video on youtube to figure this part out..
search up "how to make a port on Terraria"
Hope this help :)