Hello! I did a little tutorial on the dying process and such here if you want to read that for more detail, but in terms of avoiding hair damage I don’t bleach more often than I absolutely need to; the bleaching is what hurts the hair, the dye I use is henna based so it does no damage at all! (I use manic panic, if you’re looking for a dye brand) The bleach I use is the schwarzkopf ‘colour intense’ kind. I think I usually use atomic blonde but any of them work well!
Basically, do not bleach your hair unless you really need to, and try not to bleach right down to the root even to get shot of new growth; damage the root of the hair and it can cause it to fall out! Ammonia bleach is extremely strong, so while you might need it if you have dark coloured hair be extra careful with using it and be careful to test you aren’t allergic first. Also never leave any bleach product on for longer than the time given in the instructions, and be extremely thorough when rinsing it out- if you leave any in your hair it will continue to be active, which will damage your hair and remove any colour dye you put on it afterwards! All that said it’s a lot easier than it sounds and practice makes perfect, best of luck!