Creating the obligatory 'Hello World' example is easy. Just type the following in you editor.
function love.draw()
love.graphics.print("hello world", 200, 200)
end
Create a new folder called World somewhere in your documents and save the file as main.lua into that folder.
The easist way to get the game started is to drag the folder on the Love.exe or the Love.app.
See also: Advanced Way to Run the Game.
You should see a new window opening with the title being 'Untitled'. There should be white text on a black background saying 'hello world'.

First of all: Check every step we've done. Did you drag the folder (and not the file!) on the Löve executable?
This is very important: Read the error messages!
If the background is blue and the text says 
you probably used the wrong directory or the directory is empty.
If the looks different but the background is also blue then it is a problem with your code.

The error message will tell you in which line and near which character the problem lies. Usual causes for this are missing parentheses and extra commas.

In that case you made an error that is not a syntax error or an execution error. Look at your code. Did you copy the code from above char by char? Make sure that all the dots are there.
Great! We can now move on to begin to create our little game.