A good question. I suspect there are many answers, and maybe different answers are better for different people.
I have been praying for it to be granted/taught by God, because it is so important to our spiritual formation. I think nothing else is possible without humility.
My SF recommended that I find a Saint outstanding in particular ways that are relevant to me, and then study that Saint. And anytime I am tempted by any thought of vainglory, compare myself to that Saint. I can say this - that this worked well for me. (Not to say I've become humble, but that it is effective in combating temptations to vainglory, which is sort of the opposite of humility, so it helps.)
I've read advice from the Fathers and Saints along the way about cultivating humility - now I wish I had gathered them into one place, because I'd like to have it to read over. So I'm hoping to read more good things in response to your thread. It's a great question.
But a difficult one to answer, I think.
ETA: there is something else that came to mind, but I'm not sure I will be able to explain it well. It is a sort of realization. When I pray for the horrible things that happen in the world, I pray of course for the victims, but I pray too for the ones who commit the acts, that they will see their error, and repent, and turn to God and be saved. After praying that way for a while, something has begun to occur to me. It is that we are all sinful people. In a way, I can identify with those who commit such terrible acts - and I begin to realize that as a human being, I am no better or different. We are simply a fallen, sinful race of beings. Some may commit particular sins, and others commit other sins, and have different inclinations (if one's inclinations are better than someone else's, it is by the grace of God, so nothing to be proud over). But it is as though our differences in this way are small, while the gap between us and the holy - be it angels or God Himself - is very great. So any of us are really base along with those others who commit terrible sins. I hope this is making sense? I guess what I mean to say is that I begin to realize that simply being human - is humbling. Because we have all sinned, and fallen short of the glory of God.