Usually I start with descriptive action, move to slightly slurred speech, then add more symptoms of increasing levels of drunkenness. Unless it's a very brief description, I typically estimate the number of drinks and the effects. For an example, see "To Protect the Most Vulnerable."
Contrast that with the mouth injury in "More Hurtful Than Anything That Bleeds." To represent Vagary's split lip, I dropped the labial and bilabial consonants, but the back of his mouth is still fine so some other phonemes are unaffected.