By far the most common observations were the daily measurements that are found in the journals of Lewis and Clark as "Course...Time...Distance... Remaks. & refurncs." These were intended to be used as the early 19th century equivalent of the guide book from AAA, that tells you how to get from place to place, what sights you're going to see on the way, where to lay up at night, and where to get a good chicken-fried steak.
Course referred to the direction the expedition was traveling, stated as a compass bearing between two points. To obtain this bearing, or "azimuth," the captains used one of the pocket compasses or else the larger surveyor's compass (circumferentor) to get direction from one reference point to another--from the point of a bluff along the Missouri's north side, for example, to the tip of a prominent sandbar on the south side of the river (reference points were always identified in the journals). Their compasses registered magnetic north rather than geographic north and their readings had to be adjusted for the difference or "declination." They understood the errors that would creep in as they moved from east to west across the continent and continually adjusted the declination of their compasses to insure accuracy of readings.
Time, stated in hours and minutes, was the time required to get from the reference point used to establish the beginning of a course azimuth to the reference point marking the end of that particular compass bearing. Time was established precisely by chronometer--as long as the captains remembered to keep it wound. Because they did forget to wind it regularly there were frequent occasions when travel time was an estimate. But living as close as they did to the natural world, while still having a temporal frame of reference that included hours and minutes and seconds, reasonably accurate time estimates would have been less of a problem for them than for the native peoples who possessed few or no short-term time concepts, or for us latter-day folks who are not only more divorced from nature but have relied for so long on the watches strapped to our wrists that we find it difficult to evaluate time any other way. Still, most of the temporal observations of Lewis and Clark were obtained by timepiece--the chronometer that cost more than all the rest of their "mathematical instruments" combined.
Distance was expressed between the same two points used to derive course and time. This was normally given in miles but occasionally in yards or rods. These measurements were obtained either by pacing a course between two points or by estimating distances. Estimations are relatively easy for people having long familiarity with their environment, their own travel paces and their mode of transport. They walked about as often as they rode and this allowed them to judge both time and distances much more accurately than we can while driving a car at speeds that may vary widely (from 15 miles per hour in a school zone to 75 mph on an interstate highway).
Their sense of time and distance was more precise than ours because their survival so often depended on it and because they moved across the landscape in very different ways than we do. Throughout the expedition, the captains were reasonably accurate in their measurement of distance. They accomplished this with good guesswork, enlisted men to do the grunt work of pacing out courses, fairly sophisticated instruments and mathematical calculations, and careful attention to detail.
Remarks, or reference observations, were comments on the widths of the Missouri and the creeks and smaller rivers that entered it, the heights of bluffs or hills along the river, and–most common and most important–the identification of the reference points upon which the compass bearing/distance/direction information was based. Jefferson's directive to Lewis had included the order to note "all remarkeable points on the river, & especially at the mouths of rivers, at rapids, at islands, & other places & objects distinguished by such natural marks & characters of a durable kind, as that they may with certainty be recognised hereafter" and the captains were faithful to these instructions.