Assuming you aren't north of the Arctic Circle or south of the Antarctic Circle, you can determine your latitude my making observations throughout the course of a day, and over the course of a year. You'll need
- A rather straight stick,
- A fairly flat piece of ground,
- A plumb bob (which you can make out of string and a rock),
- Some small pebbles to mark the tip of the shadow of the stick over the course of a year at solar noon, and
- A trigonometry table or a calculator.
Use your plumb bob to ensure your stick is as close to vertical as you can make it. You'll want to place the stick in exactly the same place every day.
The first thing you'll want to find is the north-south line that passes through the base of the stick. To do this, place a pebble at the tip of the stick's shadow when the shadow is at its shortest. If you do this perfectly, you'll have the north-south line on day number one. You almost certainly won't do this perfectly, so you'll need to repeat this for a few days. Because the Sun rises more or less in the east and sets in the west, you also know which way is north and which is south. You have a compass.
You'll also have a very rough idea of your latitude. If the Sun sets to the left of the north-south line, you know you are somewhere north of 23.44 south latitude. If it sets to the right, you are south south of 23.44 north latitude.
If you want a better idea of your latitude, keep doing this until the day you see the Sun rise exactly in the East. This happens twice a year, typically on March 20 and September 23. Use a string to measure the length of the stick's shadow when the tip of the shadow crosses the north-south line. You do not need a ruler; all you need to know is the ratio of the shadow's length to the stick's length. Now it's a matter of trigonometry:
$$\phi = \arctan\left(\frac {\text{shadow length}}{\text{stick length}}\right)$$