How can one determine one's longitude and latitude without any technology or measurement tools?

With a relatively simple table of noon readings from the sun, it is possible to use cosine to calculate your latitude position (requires an understanding of trigonometry to do so fairly effectively). Longitude is easier. If you have a rather precise watch, set to universal time coordinates, and find a way to accurately determine high noon sun angle at your location. Simply verify highest sun, note it (to the second) in local time, then by subtracting your local time from UTC time, you have hours and minutes. Now, knowing that longitude is basically 15 degrees per hour, calculate your longitude.