Tiled is an open source tile map editor available at http://mapeditor.org. It is available for Mac, Windows, and Linux. As Tiled is an open source program, you can also download the source code if you want to see what is "under the hood". We are using Tiled version 0.8.1, which is the current version at the same time writing.
When you first load Tiled, you will create a new map. Go to File | New from the menu. In the New Map dialog box, configure your map like this:
For our game, we will be building our map using non-Retina assets and will later "fake" a Retina sizing. Normally, you would be building the Retina version first, and then "shrink" the map for the non-Retina version. The same techniques work both ways, so we will leave it to you to decide. Anyway, most of these settings are self-explanatory, except perhaps the "Orientation". Orthogonal is a term most people are not familiar with. Basically, it means normal square grid, aligned to the x and y axes.
You will now...