While I strongly suggest spending the extra money to have a professional do it--blonde is a notoriously tricky color to reclaim--it can be done at home using bleach and toner.
You'll need the following things, easily obtained at a place like Sally's Beauty Supply:
-powder bleach--if you have long hair, I recommend getting a tub of something like QuickBlue rather than packets.
-creme developer (I use 40-weight, but you can use anything from 20 to 50. Just ask one of the store employees which would be best for the results you want).
-toner, such as ManicPanic Virgin Snow.
-foils (if you don't want to buy foils, which make the bleach react and lighten more vigorously, just cut some tinfoil into strips).
-something to part your hair.
0. Put on gloves. Turn on your bathroom fan, and pick up anything you don't want to get bleach on by accident. Have a towel ready (one wet, one dry) in case of any mishaps!
1. Mix your bleach.
Add the powder bleach to a plastic bowl (it will react with metal!! ) and blend in your developer until you reach the desired thickness. I usually go for something like a runny toothpaste.
2. Apply vaseline around hairline, if desired. Begin to apply bleach to hair in 1/4" sections: use comb to separate, then place foil underneath section and brush on bleach, wrap foil and fold out of the way. The more closely the foil contacts your hair, the better lift you will get.
3. Set a timer and watch your lift. My hair, which is almost black, takes three 35-minute applications of bleach to reach a light gold color that can be toned to platinum. Remember: you're not trying to bleach your hair white--go for a golden tone. The toner will balance out any brassiness or golden colors you're seeing.
4. Rinse bleach. If the desired tone has not been reached, reapply in above manner.
5. Once desired tone has been reached, rinse hair. Follow directions on ManicPanic Virgin Snow to tone hair to white.
6. Condition the ever loving crap out of your hair for the rest of forever. Bleach is hella damaging, so invest in a top-shelf conditioner, like Biolage or bumble and bumble. Seriously. Brands like Aussie and Pantene do NOTHING to actually replenish hair and keep it healthy from the inside out, but merely coat it in wax and other things to make hair shiny. Pick up a high-end daily conditioner and a weekly intensive treatment, or risk severely damaged, fried hair.
This is the method I'd use to achieve a light or platinum blonde. If you're natural hair color isn't that light, I'm not sure what method I'd use. Either way, I DEFINITELY recommend letting your regular colorist fix it--blonde is a very hard color to get back.