After seeing that this is a very big topic and people often ask for help on the forums about it, i thought i would try to make a really good explanation of how to setup a minecraft server. Enjoy! (Note, this is for setting up servers on WINDOWS computers the steps are different if your on mac or linux!)

How to setup a vanilla minecraft server:

Local hosted:

1.) To setup a vanilla minecraft server on your local network (this means only people connected to your internet will be able to join it), you need to first download the server software, which can be found here: minecraft.net/download After this is downloaded, put it in a folder on your desktop and name the folder anything you want. Finally, open up the folder, and double click on the server software. this will start up the server. The first time it starts it will take along time because it has to generate all the files and worlds.

2.) After that, you can begin playing on it! If your playing on the computer the server software is running on, simply type in "localhost" for the address of the server and connect! For others to connect to the vanilla server, you need to give them the ip of the host computer. On the computer it is running on, go open up command prompt (start>run/search and type in cmd and then hit enter.) Now type in "ipconfig" and hit enter. This will bring up a lot of information. scroll through it until you find ipv4 address: the number listed there is the ip you need to give to your friends (on your network) to join. Happy crafting!

Publicly hosted:

1.) This involves more steps. Follow all of the step of the local hosted vanilla server, until you get to the part where you get the ip address from the command prompt. Write that address down, we will need it for later.

2.) Now what you need to do is go into your routers control panel, because you need to port forward. To ge to the control panel, open up cmd again, and type in "ipconfig". Below ipv4 address, there should be "Default gateway:" Take that number, and type it into your browsers url bar. If your router is setup correctly, it will bring you to the control panel. You may need to enter your routers username and password to login. If you do not know it, ask your parents for it. After you are logged in, look for a tab called "port forwarding" it may be under a tab called "applications and gaming" This is completely reliant on your router. Different routers may have different control panels. Once you have found this tab, it may ask you for an application name, if so just type in "minecraft" there should also be a box called "start" and a box called "end" Type in 25565 for both boxes. After that, there may be a drop down for "protocol" leave this at its default setting. Then there should also be a box for ip address. type in the ip address you wrote down earlier here. Finally, if there is a check box called "Enable" check it. Otherwise, click save or continue and it should save the port information there. Exit out of the control panel. Now the easiest way to find you external ip address, and what i have used is a website called ipchicken.com type this in and go to it. This website will give you your external address that your friends will connect to. After that, start up the server, have your friend type in your external ip address and connect! Happy crafting!

How to setup a bukkit server:

This is the exact process as above, only with different software. Download the software at bukkit.org . Then put it in a folder named whatever you would like. Rename the downloaded file to craftbukkit. Now this is where it changes a bit, you will need to write a start-up script. Don't worry, it is very easy. Open up a notepad document and type the following into it:

@ECHO OFF
Java -Xmx1000m -jar craftbukkit.jar
PAUSE

Save the document as RUN.bat and put the bat file into the folder with craftbukkit.jar
Finally, double click the RUN.bat file, and it should start the server. It will take a bit because it has to generate the files and worlds. After it has generated, you may either follow step 2 for local host, or follow step 2 for publicly hosted. After that is done, you and your friends should be able to play on a server together! (yay) Happy crafting!

I will update this later to include some common mistakes and solutions, and how to do other stuff such as setting up whitelisting, adding ops, adding plugins, etc.