Look up your latitude. You can find this using a paper map, but see the resources for a website that will find your latitude for you. Note it down in your notebook, as it will be used for multiple calculations for your sundial.
Plug your latitude into a website that calculates the angles for a traditional sundial. Note down the angle for the 9 am and 3 pm hours: it will be the same. You can ignore the other numbers because an ancient Egyptian sundial doesn't include them.
Find a spot in your garden that gets full sunlight. If there is anytime in the day when the light is obstructed, you will not be able to use your sundial for that time.
Using the compass, find North and make a line of pebbles about 6 inches long marking it.
Push the dowel into the dirt at the southern end of the line of pebbles about 4 inches in. Use the protractor to adjust the dowel until the angle that it makes with the ground is equal to the latitude that you noted in your note book. Pat dirt down around the dowel until it is secure.
Place another line of pebbles exactly perpendicular to the first line, centered on the point the dowel enters the dirt. Make it about 6 inches from the dowel in both directions.
Mark the quarters of your sundial at the angle that you marked in your notebook for 9 am and 3 pm. Measure the angle from the first line of pebbles in both directions. Make each of the quarter lines 6 inches long from where the dowel enters the soil.