There are two methods, named statistical analysis or Frequency analysis and pattern matching.
Note that in statistical analysis Eve should compute frequencies for $aLetter \oplus aLetter$ using some tool like this. A real historical example for frequency analysis is theusing VENOVA projectfrequency analysis is the VENONA project.
EDIT: Having statistical analysis of $aLetter \oplus aLetter$ like this says:
If a character has distribution $X$, the two characters behind $c_1 \oplus c_2$ with probability $P$ are $c_1$, $c_2$.