There seems to be some common notation for hiking and OHV trail coordinates
and I can't find it documented anywhere.  For example, if you go to
http://www.ultimatetahoe.com/archives/otherarticles/ohvtrails.htm
you'll see that the first trail is the Sand Pit, and it is referenced as 12N14.

Similarly at http://www.lanset.com/pyamagata/Captions/nspg/ellispk.html
they make reference to "NF 03" at the beginning.

I would like to know what these coordinates or references mean, and how
I can turn this into a latitude & longitude.

Hello,

The Sand Pit's trail number, 12N14, looks like the identification
number of a township. Indeed, the page "Numbering of Trails and
Secondary Forest Roads in Angeles National Forest"
(http://tchester.org/sgm/lists/anf_map_roads.html) explains how in
that forest, trail identifiers with a number on either side of a
cardinal direction are secondary Forest Service roads, and the numbers
refer to the township where the northern end of the road is. While the
Forest Service need not use the same system in a different national
forest, township number 12N14 would perfectly match the area where
Sand Pit trail is. You can see in this Topozone map
(http://www.topozone.com/map.asp?lat=38.93333&lon=-119.98333) that the
township where South Lake Tahoe is is marked "T 12 N." That means it
is the 12th township north of a survey baseline. The northernmost
point of trail 12N14 must be in the 12th township north and 14th
township east of the base point of the Mt. Diablo land survey (see
www.mdshs.org).

To convert township and range into latitude and longitude, you can
visit the Geographical Locater at
(http://www.esg.montana.edu/gl/trs-data.html). We don't know the
section where the road starts, but most townships have sections
numbered 1 to 36. Section 1 of T12N14, Mt. Diablo baseline, is at
38.9188N, 120.3622W. Section 36 of the township is at 38.8465N, while
Section 6 is at 120.4549W. Thus, the trail starts somewhere between
38.9188 and 38.8465N and between 120.3622 and 120.4549W. That would
put it in the area just southwest of Lake Tahoe.

As for the other trail, Barker Pass Road, "NF 03" simply means
National Forest Road 3. You can see it on this Forest Service map:
"http://www.r5.fs.fed.us/ltbmu/visitor/hiking/westmap.htm." You can
see that underneath the "3" on the route marker for the road is, in
really tiny letters, the old script "National Forest" logo.

I hope this information meets your needs. 

Search strategy:

California county roads
://www.google.com/search?sourceid=navclient&q=California+county+roads

California townships survey
://www.google.com/search?sourceid=navclient&q=California+townships+survey

Mt. Diablo baseline
://www.google.com/search?sourceid=navclient&q=Mt%2E+Diablo+baseline

"Barker Pass Road"
://www.google.com/search?sourceid=navclient&q=%22Barker+Pass+Road%22

Image search: national forest sign
http://images.google.com/images?hl=en&lr=&ie=ISO-8859-1&safe=off&q=national+forest+sign&sa=N&tab=wi

convert township range longitude
://www.google.com/search?sourceid=navclient&q=convert+township+range+longitude