To measure distance on topographic map you need a UTM grid, a very basic knowledge of the metric system, a little math… and dental floss.
On the UTM-gridded map below, I’ve highlighted the stretch we’re going to measure along the Thorofare Trail from the ford on the Thorofare River in the Teton Wilderness to the Thorofare Ranger Station in Yellowstone National Park. Also shown is the length of dental floss – blackened here with a magic marker to make the photography clearer – we’ll use to do the measuring.

Place one end of the length of dental floss at your start point on the map, (in this example, the ford), then use your fingertips to work the dental floss along your entire route – in this instance, the highlighted trail; in effect, tracing your route with the floss, as shown below, until you reach your end point (the Thorofare Ranger Station).

Once you’ve worked the length of floss along the entire route (or other distance), grip the start point with the thumb and forefinger of one hand and the end point with the thumb and forefinger of the other.
Place the measured length of floss against one edge of the UTM grid on the map, either north-to-south or east-to-west, whichever is more convenient, and measure its length, as shown below, using the grid as a ruler. On this particular map, each grid square is exactly 1 kilometer x 1 kilometer (1,000 meters x 1,000 meters), with the grid squares along the map’s edges graduated in 100-meter “hashmarks.” I’ve placed a mark on the length of floss’s end point, so we can see that the measured length is 5 kilometers (5,000 meters), plus 400 meters. If you operate with the metric system, you’ve determined the distance to be 5.4 kilometers and you’re finished.

For a distance in miles, it works like this. There are about six tenths of a mile in a kilometer, so to convert kilometers to miles, multiply the number of kilometers x .6, which gives us 3 miles, plus the 400 meters indicated. 100 meters is right at 110 yards, so we multiply our 400 meters x 1.1 to get 440 yards, which is 1/4 of a mile, for a final non-metric result of 3 1/4 trail miles from the ford on the Thorofare River to the Thorofare Ranger Station.
(The maps used here were generated with Terrain Navigator Pro, which creates not only the UTM grid, but the 100-meter “hashmarks,” which do not appear on “store bought” USGS topos.)
Using this approach allows you to determine distance along irregular stretches like trails or watercourses. String or yarn works just as well, but I prefer dental floss because it’s light and very strong, making it useful in other applications, such as emergency repairs and/or situations requiring small, tough cord.
A measurement like this is, of course, a simple horizontal distance that does not take terrain into account. A formula developed by the U.S. Army Research Institute is useful in dialing in ground condition to calculate the actual “effort mileage.”
Flat, scrub desert, or temperate terrain…………………………………………………………add 10%
Rolling, temperate wooded terrain………………………………………………………………..add 20%
Any loose surface material or snow (to factor in foot slippage)…………………..add 20%
Jungle or hilly temperate terrain……………………………………………………………………add 30%
Sandy desert…………………………………………………………………………………………………add 30%
Mountainous terrain……………………………………………………………………………………..add 40%