Cryptograms are solved primarily by two methods. First, pattern recognition. The easiest to recognize are single-letter words, which generally can only be A or I (or, rarely, O). Then there are a limited number of two-letter words such as IN, IS, IT, TO, AN, AT, AS, WE, HE, US, etc. One trick in particular is to look for the common TH- words, i.e. THE, THAT, THEN, THEY, THERE, THEIR.
Secondly, the successful cryptogrammer will use letter frequency to help suss out a difficult puzzle. The twelve most frequently-used letters in the English language are ETAOIN SHRDL, in that order. The least common letters are JXQZ. If you notice a certain letter being used again in again in any given cryptogram, at a frequency much higher than any other letter, its a good bet that its unencrypted form will be one of the ETAOIN group.
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