Are you bleaching or dyeing?
Bleach is a much more technical process, and the consequences of doing it wrong are potentially quite serious (burns, hair breaking off).
Hair dye though, is pretty easy.
Number one rule is that you should never try to get by with one box of dye unless you have short, fine hair. Not enough dye guarantees a patchy result. Patchiness is pretty much the main way it can go wrong.
I have long, not especially thick hair and I need two. If your partner has long very thick hair, maybe get even more.
Section the hair off. Make a ponytail out of everything but the bottom section.
Slap on the dye. You can use a tinting brush, but I tend to use my (gloved) fingers. If you’re covering roots, do the whole of the head, but aiming just to cover the roots. This is so that the roots get more time with the dye.
When you’ve done the roots for the whole head, whack the dye on the bits that are already coloured. Use a lot and really squish it in with your fingers. Shape the hair into squishy sausages and work the dye between and through the hair until it’s totally saturated. Use more than you think. Use it all! It can’t be kept (dye once mixed, will explode if in a sealed container!) Hair is a bugger for hiding pockets of dry, undyed bits, and that’s how you end up with patchiness.
Wrap it in clingfilm to develop. The heat helps and it avoids transfer stains. Clean up any splotches on the ears, neck and hairline. Don’t wait for the rinsing part because it will stain.
After the appropriate time (I have always given it a bit extra for luck - but you probably shouldn’t do that), rinse the worst out, using your hands to rub the hair and scalp, then I like to use a little shampoo (though it’s not recommended) to get the rest of the dye out. You want the water to run clear. Then slap on the conditioner, wait, and rinse again.