Tracklog
A tracklog (sometimes also called a trace, or whimsically a breadcrumb trail) is a sequential record of coordinates collected by a GNSS-capable device such as a cell phone or handheld receiver (where GNSS is short for Global Navigation Satellite System and is the generic term for GPS, Glonass, Galileo, Compass, and so on). When displayed on or linked from an expedition page, a tracklog can serve as proof of reaching coordinates, or just make an interesting visual addition. And it makes showing your work for some achievements a lot easier, too. Tracklogs can now be displayed directly on a wiki page with template:tracklog.
support and settings
It is rare now to find a device that can tell you where you are but that cannot store a tracklog to internal memory and then export it in a wireless or wired fashion. However, if you think you own one, mention it on the talk page and we'll see if we can't help you anyway. Modern devices use a standard format called GPX (because it's XML for GPS, or something); older ones may have a nonstandard one but it should be convertible. The wiki uses GPX for display so that's what you'll want.
Also check your user's manual. Many manufacturers make user manuals available on the Internet.
recording
In order to make a tracklog you need to make sure your device has this function, and has it turned on. Look through your menus or manual for tracks, track recording, track plot or something similar. If your screen displays a trail showing where you have been, then you definitely have this feature. Your GPS may already have location tracking turned on by default, even if you don't see a track displayed on the device. You probably have unknowingly recorded every move you have made with the GPS turned on since you bought it! It's analogous to Hansel and Gretel in the forest, dropping breadcrumbs, except it's not affected by birds.
Obviously you want the track log turned on, and there may be other settings too. These explanations for settings you may have. The defaults are probably fine.
Wrap when full continuously erases the oldest tracks and replaces them with the newest. This setting ensures that your GPS won't stop recording because the memory became full. There's not much reason not to use it. If you want to save your oldest tracks, copy them to your computer.
Record method selects how often the GPS saves a point on your path. You may be able to tell it to drop a breadcrumb based on the passage of time, or on distance covered. In Auto mode, if available, points will be recorded just as often as is necessary to give a good representation of your motion - more points in curves and when your speed changes often, fewer while moving in a straight line at constant speed.
Interval determines the time or distance interval between breadcrumbs. If your tracklog doesn't show as many little twists and turns of your trip as you'd like to, adjust it to record more often, or to a fine track. If your memory fills up before you have a chance to download the data, adjust it to record less often or a coarse track.
saving
Once you have moved somewhere while the GPS is turned on and track recording is turned on, you have the opportunity to Save that track. A Garmin etrex gives the choice of saving the entire track or specifying the endpoints of the saved track. The latter is quite fiddly. If you turned your GPS on at the beginning of the part you wanted to save and off at the end, it will be much easier to save the entire tracklog and then delete everything you don't want after uploading.
Once that you're sure that your GPS has recorded and saved the track, it's time to get it out of the GPS.
transferral
If your GPS receiver came with software, now's the time to break out the floppy drive, CD ROM, etc. and install it. If you didn't get one or lost it, try the manufacturer's website. You probably need to have software installed before connecting your GPS receiver to your computer.
Your GPS receiver probably has a way to connect to a computer. You could have a mini-USB port hidden under a flap as pictured. If the GPS didn't come with a cable that connects to it, you may have a camera or other device that uses the same cable. They're also cheap to buy. If your GPS receiver is part of a computing device, like an iPhone then you don't need to connect it. Skip down to your software, if someone has made that section yet.
Garmin
The Garmin product is called Map Source. Once it is installed, start the program and connect your GPS. From the Transfer menu select Receive from device. It should find your GPS. Select the check boxes to receive Waypoints and Tracks (but not Maps and Routes). Then click Receive. You'll soon have the left hand pane of the program filled with log files, representing every time you've turned the GPS on and off.
First, use Ctrl-S to save the entire thing together. The default .gdb file works fine. Then save it a second time under a new name, the name of the expedition you want a tracklog of. Now delete everything that isn't the expedition you want. Each log line is tagged with the date, so it's very easy to identify what you don't want. Just highlight and delete everything with a date other than your expedition. If you're using UTC times be careful not to be confused by the UTC date starting/ending at a different time than your local date. Do the same with waypoints not relevant to your expedition. When you've trimmed everything you don't want, save it again. You should now see your route displayed on a crude map in the right-side pane. You're now ready to upload it.
other
If you're running some freakish unsupported operating system like Haiku you probably already know where to go to look for for open source software to help you with this step, and very likely don't need a wiki help page on manipulating data.
no special software at all
Some of the more modern Garmins and other GPSs support "storage mode" and the GPX file format, so you don't need any specialized software on your computer. Just plug the GPS into your computer, and it will appear to be a USB drive. Look through the files on the drive to find the ones with the "gpx" extension, those are your trip logs. Edit them with (worse case) a text editor, or (best case) a specialized XML file editor.
Uploading tracks
(a.k.a 'sites people have used') There are multiple ways to upload your data and display it on a map to show your route. Add any you know; also, it's not a bad idea to keep copies in several places for futureproofing.
to the wiki directly
The wiki now supports GPX! Both uploading it via special:upload, and displaying it via template:tracklog.
openstreetmap.org
https://osm.org/traces/new; check out OpenStreetMap achievement#Tracklog_uploaders. OSM has four settings of tracklog privacy: private, public, trackable, and identifiable. See the link for details, but it comes down to whether each entry in the log has a timestamp or not, and whether they are chained together in the sequence they were captured or otherwise.
AllTrails.com
AllTrails.com (formerly Everytrail.com)
Displays an interactive map and track statistics. You can add travel reports, geotagged photos and the like. Reads GPX/KML/TPO files or you can upload tracks directly from the app. You can chose whether your track is public or private but there is no option (as of 2017-09) to share a private track with others.
GPS Visualizer
Open the GPS Visualizer site in your web browser. Browse to your file, accept the default Google Maps format (you can change your mind later). Upload.
Wikiloc.com
http://wikiloc.com - If you walked, cycled, canoed, sailed, or flew, wikiloc is a good place to share GPS tracks. It reads most file formats (gpx, kml, gdb and many more) and displays a map with track statistics and altitude and it integrates well with Google Earth. You can add your own text and photos. You can chose whether your track is public or private but there is no option to share a private track with others (by 2017-09; they had it before and they've been planning to add it again since 2016).
Strava
http://strava.com - If you care about how fast you got there, and want to compete in a spiral of painful exercise with friends - or complete strangers - Strava is ideal. It reads most file formats and displays a map with track statistics and altitude, as well as showing power exertion and the like.
mygpsfiles.com together with Dropbox.com
mygpsfiles.com - myGPSfiles lets you visualize your tracks (only gpx/tcx/crs/fit format) on a map, but the tracks are not kept for more than one month. If you want to permanently have access to the tracks, you can upload your tracks to a Dropbox.com folder (with sharing-link enabled) and visualize the complete folder at once with mygpsfiles. If you want to show only one track, you can modify the instructions from the website and use the url to a single file instead of to a folder. Waypoints and geoCashes are ignored by the software so the maps won't show the hashpoint.
VFRplanner
vfrplanner.co.za (iDevices only, formerly vfrplanner.org/app)
This site looks like it is for plane pilots but the website talks about the feature to upload track logs and view them on a map. The tracks can be set to public, private or "shared by link". (not tested)