Converting a road bike into a fixed gear can be as simple as purchasing a fixed wheel for the rear and swapping that out with the geared wheel, removing all the stuff that shifts gears, and converting the crank to a single.

In many cases running the chain ring in the middle of the spider will give a near optimal chain line and in other cases one might want to install a narrower bottom bracket so they can run the single chain ring on the outside of the spider... shorter stack bolts or spacers will be required to do this.

Benefits would include a bike that has a geometry that is better suited for the road and the ability to run fenders if you plan to ride in wet or snowy weather.