The trick to doing this well tends to happen during the rewrite stage for me, but it could happen in planning too. Take a look at the beginning of your story/chapter/scene and look for opportunities to apply circularity. Ask yourself, "What can I bring back that will be necessary or fun? What loose ends need tied up?"
Circularity in your characters
Character traits can create circularity. For example, in the book Because of Winn Dixie, we learn early on that the dog hates thunder storms, which makes it all the more powerful when the storm comes at the end of the book and Opal can't find the dog. In my book Replication, Martyr's sacrificial nature comes back in a big way. Giving is a big part of who he is, so the reader isn't a bit surprised that he'd make the choice he made. And it makes the reader like him even more.
Circularity in your dialogue
Circularity in dialogue is fun because it's how people talk in real life. It's the inside jokes we use with our friends. Those, "You had to be there" moments. When you create inside jokes in your story that your reader gets, it makes him happy.
You can also set things up in dialogue to come back later. Clues. Plot twists. Resolutions. In my book The New Recruit, Gabe suggests that Spencer would be the best person to reach out to Pasha, which makes Spencer angry at the time. Then later, when Spencer is reaching out to Pasha, he thinks back on that conversation with Gabe with a "Well, what do you know?"-type of attitude.
Circularity in your narrative
The movie Zombieland does circularity fabulously with the rules that flash on the screen. The main character explains the rules in the beginning narrative of the movie, but as the movie goes on, whenever he survives a hairy situation, the rule flashes on screen again. Beware of bathrooms. Cardio. Double-tap.
Circularity in your plot
Pride and Prejudice has a ton of circularity. It is so fabulous. (I just watched it--again--last weekend when my husband was out of town.) This story is all about misunderstandings that come back around to reveal the truth.
And one of my all-time favorite examples of circularity: Harry Potter and the Prisoner of Azkaban. That WHOLE ending is fabulous. From the point of going to Hagrid's hut to give one last farewell to Buckbeak and onward, we see it all happen, and then we see it all happen again from a different vantage point. Brilliant.
Circularity isn't always a positive/positive set up. Sometimes it's the opposite. A great trick with character development is--somewhere near the beginning of the story, whether in narrative or dialogue--to have your character say, "I'll never do that," then by the end of the story, make them do it. Find a way to change them through the course of the story.
Practice looking for circularity when you watch TV. This can sometimes be all too easy if the shows aren't well-written. When watching detective shows, my husband always says, "He did it!" when a nobody has a tiny speaking part early on. Hollywood likes to save money, and if an actor speaks, they make a lot more money. So when small characters speak early on, they tend to play a bigger role later. See what other types of circularity you can find in your favorite shows.
Circularity doesn't only happen at the end. Circles come in all sizes. One of my favorite small circles from my Blood of Kings trilogy is when Vrell uses the leg sweep on Achan. He'd been trying to teach it to her for weeks when he thought she was a boy, and she could never manage it. And then, at the best possible moment, she get him good. It's a great moment, and the reader smiles big. That tiny subplot came full circle and it was worth the extra effort it took to write it all into the story.
Have you used circularity in your stories? Share how. Or give me an example of circularity from a book, movie, or TV show.