Lightening hair (in my opinion) the harshest way to color hair and it does the most amount of damage. However if you dream of blonde hair and nothing else will make you happy, then I can help you out with a few tips. These tips will minimize the damage you do.
Before I start talking about chemical ways to lighten hair, I want to mention that there are natural, gentler ways to do this. Of course this also means it is slower and doesn't lighten much at a time, but in case anyone wants options here they are: Honey Lightening and Cinnamon. I would not recommend lemon juice, it is as bad if not worse than chemical hair dye.
The most important thing you will need is: coconut oil (extra virgin is the best one for this). I love coconut oil, it does so many awesome things and it's so cheap. Anywho, coconut oil can protect your hair against damage while bleaching. The oil must be added to your entire hair and left to sit on it for an hour (to allow it to penetrate the hair) then you bleach on top of the oiled hair, do NOT wash out the oil first. No it won't ruin the hair color and yes it will prevent a lot of the damage. Here is a very long thread about how it is used and people's experiences with it: Possible way to protect hair from conventional peroxide damage. P.S. it also works for any other chemical hair dye that uses peroxide as a developer.
Gentler unnatural alternatives to bleach are: Sun-In
(which has peroxide) and Go Blonder
(which also has peroxide); these should be used with coconut oil.
The second most important thing to keep in mind is roots only. Once the initial lightening was done, any future coloring should be focused on roots only. Even the instructions that come with the dye say so, but it's worth mentioning. The more you lighten the same hair (section) the more you damage it, the more it breaks, the thinner and drier your hair gets. And make sure you use coconut oil every single time you color, this isn't a once only type of thing.
Now that you can color and maintain your color with minimal damage thanks to coconut oil let's talk about the hair color itself. Lightening hair can easily cause brassy/orange tones. Fortunately for you there is an easy and non-damaging way to deal with that. In order to combat the orange you need blue, blue will make your hair take on a more ashy tone rather than brassy. For this I can think of 3 options off the top of my head (heheh): blue/violet shampoos, toners and blue manic panic. For toners you can use coconut oil if it comes with a developer, other than that here are some instructions: How to Use Hair Toner to Remove Brassiness. Shampoos are pretty self-explanatory, here is an example: NEXXUS Toning Shampoo
. You can mix some blue manic panic into your conditioner to keep the brassiness out, but you have to be careful not to end up with blue hair, so its more for advanced users.
Cassia obovata is a very important way to condition, strengthen and give shine to hair. I have an extensive entry on it, but one warning: it adds golden tones to light colored hair, so if you don't want golden hair use an acidic liquid to mix it with and apply it to your hair right after its been mixed (so the dye is not released) also do not leave it on your hair longer than an hour. Alternatively you may want to avoid cassia (maybe) and use an over the counter gloss. You can find my entry on cassia here: All about cassia obovada, henna, indigo.
Other things that help with maintaining your hair as healthy and thick as possible during this process are: conditioner only washes, gentle handing, oiling, satin pillow cases, deep conditioning treatments, protein treatments, regular trims, etc. A lot of this information is here: What you need to know about growing long healthy hair.; the rest is here: FrannyG hair care.
There is also a very extensive forum thread where different people talk about their methods and how it worked out for them, if you want to read more: Bottle blonde grows long.
Keep in mind that no matter how much you take care of your hair, it is still being damaged by the process, so if you're trying to grow it out longer, expect it to be very very slow, especially if you have fine hair.
Last but not least, love your hair and your hair color. Enjoy it! :)