Most date the expedition to a period running from the late summer/autumn of 460 and through the end of the summer of 459 BCE. What we know about it is: not much. Thucydides gives an account which seems muddled and vague. Diodorus gives a similar effort. We have a casualty list (an inscription on stone) which records that there was a campaign to Cyprus, Egypt, and Phoenicia. Between the various confused accounts, we get the impression that this fits into a larger theme of "Delian League" (read: Athenian) military adventurism in the hey-day of the mid-5th century, when the League still ostensibly made collective decisions. In this case, it seems that Inaros II (an Egyptian aristocrat in exile who stirred a rebellion against Persian rule there) approached the Greeks, possibly a cabal of admirals, when they were in Cyprus and invited them to help in Egypt. The Greeks, perhaps under a certain Charitimides, answered the call but were eventually defeated by the Persian backlash. Inaros II was taken prisoner and hauled away to Susa. Thucydides paints this as a major disaster for the Greeks, but none of the sketchy sources can get the numbers right as far as thousands of men or numbers of ships involved.

You can read the account of Diodorus Siculus here, starting about paragraph 74, and keeping in mind that Diodorus was writing 400 years later, did not always have access to the best contemporary source material, and was not above embellishment to make his stories better.