Not Chinese, but I have experience adapting traditional Chinese learning methods so that I could learn Literary Chinese (think of it as to East Asia as Latin [and Greek] has been to Europe), as well as academic knowledge of some of this from China studies and Linguistics at a graduate level.
Memorisation is largely just wrote. They repeat something until it sticks. Charactera are learned largely stroke by stroke by writing them out a ton, and many things are similar. A lot of literature is memorised verbatim.
Surprisingly, up to a point, this is actually really effwctive. And especially for young children, who can not only accept a lot of repitition, but often get a lot of joy out of it, it's very effective.
I myself even as an adult have managed to memorise dozens of poems in Literary Chinese, and even some prose. Once you get started it becomes quite addictive.
One way they make this easier though is similar to what things like Sesame Street and Play School do here. Put thjbgs to song.
Chinese language YouTube is full of videos with cute little animations, with ancient poetry set to music. Kids learn to sing along and do a little dance while they memorise 3,000 years of canon poetry and short prose. I've found these resources massively helpful.
At a certain point, once you've memorised enough of the stuff, you start being able to understand more and more novel material.
Edit: To reiterate, this works up to a point. Chinese education tends to use this hammer even when a screwdriver would be more appropriate, and for specific things there are more effective strategies. But especially for young children, a level of wrote memorisation with aids to make it more stimulating and fun is extremely effective for almost anything.