Absolutely, you can do this. This goes a bit beyond what this particular forum covers most of the time, however. Folks usually talk about map designs over on the trailbuilding forum. Nowhere really addresses the mechanics of it because you can get an entire university degree in it (I'm working on a master's level minor in it, myself).
As far as the basics go, there are a few things you need:
GPS
Mapping software (often called GIS or geographic information systems software)
possibly another program to download/convert your GPS data into a file format easily used by your GIS program of choice.
Probably most simply, you would need a program like National Geographic Topo! with topo map data included already. This software package prints really well with coordinates in the margins, a declination adjustment, and grid markers so people could even use a compass to navigate the area and optionally an elevation profile.
Example:
You can get much more advanced and complicated, too.
This one is a work in progress (an old work in progress that never got completed). It's being made in ESRI's ArcGIS (a very expensive software package). In it are a combination of paved trails, gravel roads, wide trails, and singletrack. There is also raw GPS data and there are finalized files (raw GPS tracks are frequently inaccurate in places, so I like to collect multiple tracks of each trail in order to average for the best possible path).
Some people take their raw GPS data and stylize it in Adobe Illustrator. There are examples of that in the trailbuilding forum.
