How can I measure the population growth of yeast?
The standard way to measure growth in a liquid culture is to measure the optical density (OD) of the solution – basically, how cloudy it is. Bacteria or yeast in a solution will absorb light that passes through it, making it more cloudy (or turbid). Within a certain range of turbidity, the OD of the solution is directly proportional to the concentration of organisms in the solution, and you can use it to accurately estimate the population in your sample. Outside of this range, you'll need to accurately dilute your sample to get it into this linear range.

Generally, we use a spectrophotometer to measure absorbance of red-orange light (this is called OD 600, for optical density for light with a wavelength of 600nm). A google search turns up a number of plans to make cheap, homemade spectrophotometers that could let you take these measurements without having access to a lab, though I can't speak to how accurate they may be. You might also look at home-brewing supplies, as brewers are also interested in measuring yeast growth and tend to have lower budgets than molecular biologists.

You only need a spectrophotometer that uses visible light to measure bacterial/yeast growth. Many specs also work in the UV spectrum which allows them to measure DNA concentration, but you won't need that.