For a US haircut, the common guideline is 15% to 20% of the pre-tax price, so on $60 that's roughly $9 to $12. Many people round up to $10 or $12 for a good cut, and tip a bit more if the stylist did something elaborate or you're a regular.
There's no strong research on exact haircut tipping amounts that I know of, so treat these as social norms rather than findings. Customs differ elsewhere: in many countries, including Japan, tipping isn't expected at all.
If you're tipping in cash, handing it directly to your stylist at the end is the most reliable way they receive it, since some salons pool card tips.