Practice
Memory feats centred around numbers can be performed by experts who have learned a 'vocabulary' of at least 1 image for every 1 and 2 digit numbers which can be combined to form narratives. To learn a vocabulary of 3 digit numbers is harder because for each extra digit 10 times more images need to be learned, but many mnemonists use a set of 1000 images. Combination of images into a narrative is easier to do rapidly than is forming a coherent, grammatical sentence. This pre-memorisation and practice at forming images reduces the time required to think up a good imaginary object and create a strong memorable impression of it. The best words for this purpose are usually nouns, especially those for distinctive objects which make a strong impression on a variety of senses (e.g. a "Lime" for 53, its taste, its smell, its colour and even its texture are distinctive) or which move (like an "arrow" for 4). For basic proficiency a large vocabulary of image words isn't really necessary since, when the table above is reliably learned, it is easy to form your own words ad hoc.
Memorization of base set is much easier using Anki flashcards.
Read more about this topic: Mnemonic Major System
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“Those who make a practice of comparing human actions are never so perplexed as when they try to see them as a whole and in the same light; for they commonly contradict each other so strangely that it seems impossible that they have come from the same shop.”
—Michel de Montaigne (1533–1592)