First of all: it's gonna be a long way. Keep this in mind while reading on.
It took me nearly a year to manage the right color and everything. And to start with you really need a very robust hair structure, which I - lucky me - have.
#1: Dye your hair with the strongest blonde dyeing thing you can get in your local drugstore. I can recommand a few: Poly Palette, Nutrisse, Schwarzkopf Blonde (I'll check the numbers and exact names later). There are of course other colorations, like bleaching powder for example, but you can only purchase those in special hairdresser shops. But go for it and have a try. I would be very interessted in it.
#2: If you're not naturally blonde the whole process will last even longer. Yeah and there might be some hat-wearing phasis included. I guaranty for nothing. Someday I read an article about Ashlee Simpson wanting her natural hair color back after she dyed it black in an act of protest because of her sister Jessica. It took her 5 dyeing sessions in a row to get the blonde back. And it was all dirty red in the meantime. So think of that. But my advise is: Don't do 5 sessions in a row. Your hair will be like shit after that. I did it once with 2 sessions and a day between - and that was already a hard thing to cope with for my hair.
#3: With reaching the right lightness it's not enough. It happens that the bleached hair gets an ugly shade of orange or yellow (which also karl described in his comment). But I found a solution for this nasty thing. You have to treat your hair with special shampoo and other styling products. The special thing is it has to be shampoo for white or grey hair. No kidding. It really works. I use "Guhl Révité". The shampoo is purple. That's why it's able to reduce the yellow shade. Kind of a chemical thing, I guess. They - the colors - cancel each other out in some way. I think it's simply because of this complementary color thing. I also used "John Frieda's Sheer Blonde" styling mousse "Star Blonde". But I changed it to some cheaper Schwarzkopf thing. And once a week I use a silver coloration for grey hair.
Update: I finally found the piece of paper where I once wrote down the brand and number of the silver coloration I used. It's: Londa Londeston Easy Colors "Silver Shine" Nr. 89. It'a a easy-to-use mousse coloration, and by the way it's a very cheap one to. You can get it for only € 1,95. You can use it 2-3 times, depending on your hair structure and how many hair you got. It really worked. But be careful with how long you're keeping it in your hair. I once forgot to rinse it out in time and then my hair had quite visible shade of purple. But this was over by the next time I washed my hair again.