The matchmaker visiting times are 10:30 AM, 3:00 PM, and 7:00 PM. She will visit at these times for three days, begining a couple of days after your Tamagotchi character becomes an adult.
If you have a V4, the matchmaker visits for a total of about 10 seconds unless you press a key as soon as you see her. If you don't press a button within that 10 seconds, she's gone until the next scheduled visit.
If your Tamagotchi character hasn't turned into an oldie yet, and s/he has been an adult for a couple of days, you can force the matchmaker to visit by setting your Tamagotchi's time to 10:29 AM, 2:59 PM, or 6:59 PM. Then wait. She will appear in 1 minute.