If you are wanting to install a New Minecraft Server at home there are a huge number of online guides and tutorials to get you going. Below are the basic steps to just let you know what is involved to have a running server.
Download the latest Java - Download and install the latest java to make sure you are up to date.
Download Minecraft_Server.jar - As Minecraft is written in java you will need to download a version of Minecraft
Create a Batch file - This is like a shortcut on your desktop so you New Minecraft Server is easy to start up with the right commands.
Agree to the EULA - You will need to confim that you have read the End User License Agreement but editing the file and changing the line that has eula=false to be eula=true
Launch your server - Double click on your batch file that you created in Step 3
Join you new server - It's time to checkout all your hard work so launch your Minecraft client and connect to the Multiplayer with the Server address as localhost
From this point the server is actually up and running but only you can connect and play. Further details on the network setup required is below:
Setup Port Forwarding - Much like when you telephone a large company and are stopped by the receptionist. Then you get asked to be put through to a person that works inside the building. From the Servers perspective it needs to talk to/through your router that leads out to the internet. By configuring this connection (port forward) people can be sent too and from your server.
Confirm you IP Address - This is quick and simple by doing a google search on "What is my IP Address". What will be returned is the address people need to play on your server.
Get Players - Ask your other fellow players to connect using the IP Address that you have identified in Step 8.
Modify your server.properties file (if needed) - Minecraft Wiki has all of the settings you may need to change but as a guide:
gamemode=survival: change this to gamemode=creative to put your server in creative mode.
max‐players=20: change this number to increase or decrease the number of players that can join your server at one time.