If you want me to show bukkit/forge servers, then mention it, because those are more complex.
Server

First, Vanilla
Download the jar from here
https://minecraft.net/en-us/download/server
Create a text document, put in the command
java -Xmx2G -Xms1G -jar minecraft_server.1.12.2.jar nogui
PAUSE
Change the numbers depending on how much RAM you have, and the section with minecraft_server.1.12.2.jar should be changed depending on the version of the server.
Save the text document as run.bat
Double click the saved run.bat file
Server not going to run fully first time, open Eula file, change it to true
Then run it again. It should generate all of the files needed for the server.
Then you need to port forward, this part I'm not going to go into because it's different for each internet provider, but what it does is allow people to access the server, otherwise a firewall is blocking the port. The minecraft server port is usually 25565
Use this to check if port 25565 is open: http://www.portchecktool.com/
The ip used in the port checker is the ip we need to use to access the server, then have :25565 after the ip.
Send the ip, and we should be able to access it.
Download it. Paste the command in notebook. Save as that thigny. Open. Close. Open ELua. Change to 'true'. Run. Check your port. TADA! You're done.

My computer won't be able to host a server... It doesn't like it when I play with my brother over a local area network.

Some of this stuff is pretty hacky, especially port forwarding, which can leave your computer open to viruses (there's a reason for the firewall block!). You sure this is a good idea? There must be an easier way to host a MC server...
In any case, just be careful when you go for it. Keep in mind these things too:
- Not all Operating systems run batch files properly: some, like more recent Microsoft versions, may limit the use of batch files to prevent the spread of some basic viruses, and some unix-based operating systems like Linux and Mac won't run them at all.
- Screwing around with the EULA can have some legal repercussions.
- It may be easier to leave out "nogui", and do it graphically. Command line usage can be tedious if you're just learning it.
Good luck, and thanks, Tony!
First, Vanilla
Download the jar from here
https://minecraft.net/en-us/download/server
Create a text document, put in the command
java -Xmx2G -Xms1G -jar minecraft_server.1.12.2.jar nogui
PAUSE
Change the numbers depending on how much RAM you have, and the section with minecraft_server.1.12.2.jar should be changed depending on the version of the server.
Save the text document as run.bat
Double click the saved run.bat file
Server not going to run fully first time, open Eula file, change it to true
Then run it again. It should generate all of the files needed for the server.
Then you need to port forward, this part I'm not going to go into because it's different for each internet provider, but what it does is allow people to access the server, otherwise a firewall is blocking the port. The minecraft server port is usually 25565
Use this to check if port 25565 is open: http://www.portchecktool.com/
The ip used in the port checker is the ip we need to use to access the server, then have :25565 after the ip.
Send the ip, and we should be able to access it.