Minecraft, runs on a platform called Java. Java comes in many shapes, and forms, which may make it confusing exactly which version of it you should have installed, which is what this should hopefully explain.
First, we want to find out our OS's processor architecture.
If you are on Windows - Press your Windows + R keys, to bring up a run dialogue, in it, type in: "cmd", and hit enter. This will bring up a command prompt window. In the window, type in:
echo %processor_architecture% then hit enter. If the output was amd64, you have a 64-bit OS. If the output was x86, you have a 32-bit OS.
If you are on Mac OSX - You have a 64-bit OS. If you're running OS X 10.6.8 and below, stop here and use to update Java instead. Otherwise, you can continue.
If you are on Linux - Type this command in a terminal window:
Now that we have that, look at the diagram below, and download the proper Java version for your OS and processor architecture. If you are prompted that said version of Java is already installed, please uninstall your current version of Java and redo this step.
Once you have installed the proper Java version, you should give the game a go!