There are numerous ways to do it. The most convenient way might be the flow cytometry if you have the machine in your lab. Choose a dye to indicate the integrity or viability of your cells and do the cytometry. For example, use a Propidium Iodide dye to stain your dead cells. Then the cytometry machine will tell you the total number of cells and dead cells. You can then calculate the number of viable cells. The whole experiment can be accomplished in 1-2 hours.
If you do not have access to a flow cytometer, you can stain the cells with propidium iodide (which stains dead cells) and SYTO9 to stain living cells. After staining place about 25 microliters of the stained yeast suspension on a hemocytometer and count.
The results will not only allow you to note how many cells/ml you have but also what the proportion of live to dead cells is.
the most accurate and reliable method for seeing viable Cells is Colony Forming Units (CFU) /ml. Make serial dilution of the desired sample and you can go for pour plating by adding 10-100ul serially diluted sample to petriplate. Incubate for 24 hours and count next day the colonies formed on PDA.
You can use Methylene blue. The dead cells absorb the blue color. Using a neubauer chamber, you can differentiate between living cells and dead cells. There are many methodologies for the proper use of the neubauer chamber.
With the help of CFU you will get the no. of viable cells only. With methylele blue dye exclusion you can calculate the %viability as you count the live cells, dead cells from the total loaded cells on neubauer chamber. Plus you also get the total no. of cells/ml and no need for separate method to calculate total no. of cells. With proper handling techniques you get reproducible results with this method. This is useful when you are following growth rate kinetics.