How to make a paint image have a transparent background instead of a white background?

Ok, so I play a game called Minecraft. You don't have to know what it is. But basically, in the game you can change the textures of any item/weapon you want by going into the texture file and editing it in a paint program. I changed a weapon in Minecraft using MS Paint. The file of the weapon is basically a white square with the weapon displayed in the middle. The problem about this is that when I open up MInecraft, the weapon is pretty much a white square with the weapon in the middle. That's not what I want, I want it to only show the weapon and not the white square. The reason why it did that was because I pressed cut on certain areas, making the background white technically, so it shows up in game as a white square. How can I make it so I save the image so the background isn't white, but transparent?

Try saving them as a PNG or download Paint.net or get a trail of Adobe Photoshop for advanced editing.