As an employed, commission based hairstylist with a T4, where within the Turbo Tax system do I claim the tools, courses, and other employee expenses?

What box is your income in on your T4?

If it's employment income (Box 14), then you need a T2200 from your employer to be able to claim employment expenses. 

If the income is on Box 83 - Barbers or hairdressers, then you are considered to be self-employed, and can enter your expenses in that section of the return. Please note that Self-Employed expense claiming will be available on February 14 in TurboTax Online.