Particularly for students who learn best from listening, you can tie many uses of commas and other punctuation to the inflected patterns in spoken speech. For example, when reading a sentence with an appositive set off by commas, pause for an extra beat when you reach the commas: "Paul, the man's best friend, lived next door." While it would be unnatural to maintain such an exaggerated reading style for all your read aloud activities, dedicate several minutes to this exercise at the beginning of all reading activities. Have students do the same, helping them to recognize proper punctuation and comma use.
While "drilling" often connotes dreary and old-fashioned learning practices, it can serve a useful role in helping students to integrate their lessons on punctuation. You can make comma drills slightly more interesting by providing engaging and relevant example sentences for students to punctuate with commas. For example, instead of providing the generic "Farmer Ted has cows pigs and chickens," ask students to add commas appropriately to a sentence featuring yourself or someone from your classroom: "Miss Fern has red hair blue eyes and big feet."
As students read, find concrete ways for them to note proper comma use. For example, if you read to the class during a circle time activity, select large format books so that the class can read along. For a dedicated "comma time," have students raise their hands every time you come to a comma. While it would be impractical to give students feedback at every comma, you can stop every so often and praise the students who correctly noticed the comma use.
Encourage students to "rehearse" using commas and other forms of punctuation by framing notebook or diary writing activities as a form of practice. Instead of intimidating students with a looming red pen, encourage them to experiment in their notebooks. While early stages may evidence overuse or misuse of commas, you'll prevent the common problem of writing wholly devoid of punctuation. Monitor notebooks to check students' progress with commas, introducing more practice activities as necessary.