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 becomes an adult.
On the V4 you have to watch carefully, and be prepared. She beeps as she's crossing the screen. If you don't press a button to stop her, she won't stop. (If you miss her, you can try again by setting your Tamagotchi's clock to 1 minute before one of the times I mentioned above, then wait for her to appear when the clock ticks over.)
Once she does stop, she'll open her book, show you a picture of the prospective mate, and ask you "Love - Yes / No" Select Yes to have your Tamagotchi character mate with the one offered by the matchmaker, or select No to reject her offer.