Most common letters
The simplest and most effective strategy is to guess the most common letters first. In English, these are E, T, A, O, I, N, S, H, R and D, listed from most common to least common. If your opponent has chosen a word or phrase in English, choosing these letters will maximize your odds of getting one right.
Vowels first
Another effective method is to guess all five of the vowels including Y first. After all, the number of words your opponent could have chosen without any vowels in them is very, very small. This strategy should guarantee you at least one correct letter, and knowing the vowels will go far to help you guess the words.
Letter pairings
Certain letters frequently come hand in hand with other letters or letter combinations. For example, Q is almost always followed by U. In English, the most common pairs of letters are TH, HE, AN, RE, ER, IN, ON, AT, ND and ST, again listed from most to least common. Think about where in the word these would go, as well. For example, ER would be a logical pair at the end of a word, while TH would be expected at the beginning or end, and less often in the middle.
Short words
Does the phrase you are guessing contain any one-, two- or three-letter words? If so, guess letters that you would see in common short words. A single letter can be either A or I, and nothing else. Common two letter words are OF, TO, IN, IT, IS, BE, AS, AT, SO and WE. Common three letter words are THE, AND, FOR, ARE, BUT, NOT, YOU, ALL, ANY and CAN.