First thing you need to do is actually get your town to open up Shampoodle. The way to do that does require a lot of gameplay and spending money. First you need to spend at least 10,000 bells in the Able Sisters store, my advice would be to just buy everything and add it up as you go along and also the store Kicks needs to have been unlocked and been open for at least 7 days before Shampoodle will become available. Apparently it takes 4 days to build. If you wish to, you can easily skip through all that by adjusting the date/time on your console (although it is cheating! I'm guilty of doing it!)
Now onto the customising part, you pay 3,000 bells and it can only be done once a day, so if it goes wrong you'll have to wait. To prevent any heartache there is a hair chart here to help with the answers to give for the results you want.
To get the hair style for my character I answered the following:
Hair
1) Use the scroll bar to almost the top, Harriet will say something like "a bit on the casual side then"
2) Answer: "My room is clean!"
3) Answer: "I like to style my hair!"
