I'm not a professional but I've learned through many trial and errors enough to know what works and what doesn't. The best advice that I can give you is to not buy the boxed dyes/bleaching kits that you see at your general stores like Walmart, Target etc. Most of them are pretty damaging for your hair, and there are definitely better options available out there. If you're interested in actually lightening your hair, get 1-2(depending on how long your hair is) hair lightening packets from your local beauty salon store or on amazon.com for around $5. They're known as bleach to most people. I prefer the
SalonCare Prism Lites brand. I think the "
Blue Packet" would work best for you as your hair is black, and since you want to go for an
ash tone, the cool tones in the lightener would help you. You don't even have to do your roots if you feel like your roots will be damaged. Just get your household aluminum foil.. line it with pieces of your hair, and then apply the bleach close to your roots but not close enough to the point where the bleach can get on your scalp. Bleach also process super quick nearer to your scalp due to heat so you'll probably want to do your ends first and then work your way up.
The next step is to find a creme developer that will help assist with the bleach. You can just do a quick research to find ones that will work for you but there are many brands out there including SalonCare lol. All developers are sold in levels of 10, 20, 30, and 40. Since you're just going brunette and don't want to damage your hair, get a creme developer in
10 volume. That's the lowest level you can get with bleaching, and the least damaging. I personally like to use 20 volume since it gives me the level of lightness that I want but it's all personal preferences.
After you mix the creme developer with your bleach and apply it to your hair, your hair color will get a little lighter(a brownish orange tint). Then you can just apply whichever dye you want ontop of your new bleached hair. If you don't want your hair to be damaged, try to go for ammonia free or semi permanent dyes as they are "healthier" for your hair. You can also get those from your local beauty salon store, amazon, or anywhere else online. They come in liquid form or creme. Both works great but I prefer creme dyes more. Once you open your dye tube, mix it accordingly to the instruction rules with the 10 volume creme developer that you used with the bleach earlier. Most dyes are 2 to 1 ratio so it's pretty easy to figure out how much you'll be using. And since dyes always turn out darker than the box shows, I'd still suggest buying a color that is slightly lighter than the color that you want to achieve. The last step is to get a nice hair conditioning mask(or make your own) that will also lock in the moisture of your hair as well as the color.
You can always buy Japanese hair dye boxes if you don't want to bleach your own hair. They're meant for people with darker hair, and they did somewhat lighten my hair without the bleach but I felt like they made my hair super dry. Other than that, everyone's hair needs some TLC so if you treat your hair well, then you shouldn't have a problem at all with coloring it.. regardless if it's from chemicals(shampoo ingredients/dyes/etc), heat damage(sun/curling/straightening tools), or whatever other reasoning. Good luck on your process if you ever decide to go lighter!