Limit what you try to cover in one session. Explaining one big category is plenty to cover in a session. Or if you are working with a student who has four sub-types of sentence-punctuation errors, you might be able to cover two, but probably not more than that. Make sure he understands that working through all the categories could take several weeks.
Keep checking on what the student understands and can do. Ask the student to explain the concept back to you in her own words. Ask the student to write a new sentence using the concept correctly. Don't just assume that she has understood everything you've said, because she may be pattern-matching on the wrong pattern as she edits sentences. Although students will often balk at it, work hard to get them to explain to you in detail what they're thinking as they're editing after they seem to have the concept under control.
Only if a student needs more practice after you've gone through all the examples of a type of error in his paper should you turn to the handouts or textbooks for exercises when you're doing this type of teaching. Students are often much more proficient at spotting errors in texts they haven't written and will miss exactly the same problem in their own papers time and again.
ESL students will be especially frustrated by their non-idiomatic use of language. You'll get frustrated too because native speakers often can't articulate why our idioms are the way they are. Warn especially those students who struggle with article usage and idiomatic phrasing that they may need an editor until they become more experienced at listening and reading so that they can intuit idiomatic levels of language.
If you have an ESL student who's struggling with articles and tense endings, don't be afraid to admit when you've reached the limit of your explanations. Sometimes students need to hear similar explanations in slightly different language from another tutor, teacher, or editor before they'll understand the point. Sometimes I just punt and send the student to an ESL program for a more expert explanation.