How do I snap the Unity camera to a 2D, tile-based map?

I have a 2D, tile-based map. I want to be able to control the number of visible tiles on the screen vertically and horizontally, regardless of resolution. I want the player to be able to move the camera one tile width at a time until it hits the edge.

I do not understand how to manipulate the Unity camera in order to accomplish this. I have read the documentation, and Googled, but there is just something that is not clicking for me.

So, let's say I have a 100x100 map. A 32x24 portion of the map is shown at a resolution of 1024x768, each tile has a size of 1x1 Unity unit. The bottom-left of the visible area of the map starts at the bottom-left of the map (0, 0). The player then clicks the right arrow key and the map moves one tile to the right (1, 0).

How do I accomplish this, given that I am using the latest version of Unity in 2D mode?