I just had a story called Even Steven that was published on lush today (or maybe it's yesterday by now). How you transition is a matter of where you are and where you need to go. I know that doesn't really help much. But if you read Even Steven you'll get some idea of how it can be done. And here are some notes to guide you through he story.
The first section of the story lays out the central dramatic conflict. In this case, what happened then and what is happen now. We put the two characters (who've not seen each other between then and now) in touch. We set up a little of what's happening in the present (attending a wedding), relate that to what's happening between the two characters. Then we move ten years back. It's simply a matter of writing: "The unfinished business." (Yes, I know it's a sentence fragment, but it's what works best there) and we're off into what happened ten years before. Of course, I had to make sure I'd introduced at the beginning of the story that there was something unsettle between these two, so the reference to "unfinished business" is just a matter of going back to something mentioned earlier (and hopefully the reader has been wondering about).
After we go through what happened ten years before we come to the first big transition.
In the first section we had Annie and Bradley in the past and Annie and Bradley in the present. Now at this big transition we're moving on to Annie and Ginny in the present. You'll notice I always like to use some visual clue to a big transition - usually three centered asterisks. That first paragraph after the asterisks is an illustration of one way to handle the transition - we've moved from Saturday night before the asterisks to Sunday morning after and we do two things in the first paragraph: mention what went before (a reference to the wedding) and then on to the new character. You'll notice I spent a paragraph in the first section of the story talking a little about Ginny, Annie and Ginny's meeting, and the nature of Annie and Ginny's relationship. That is important so that so important a character as Ginny doesn't just suddenly appear from thin air.
In the second section of the story we go through this conversation/interaction Annie and Ginny have over coffee and pastries - the tension rising as Annie tells Ginny about what she's done, the relation to Ginny's past, etc. And we finish the section with Ginny leaving and some hard feelings between the friends.
We then come to the second big transition to the third section, again using the asterisks.
In the beginning of the third section I do what I didn't do at the beginning of the second section - drop a completely new and unanticipated character into the story. But that is another way to do a transition - get the reader wondering about a new character. There is no preparation for Pat. In the first sentence of the third section she's just talking and there's no immediate explanation of who she is or why she's in the story. It's a full page before we find out the who and why of Pat. I felt I could handle Pat differently from Ginny - Ginny is a major character with a major interaction with Annie, but Pat is just a minor character, so we can be a little loose with her. Also. It makes sense that Annie might want to see a counselor over the central conflict in the story, so Pat makes sense. But really Pat's only real function in the story is to supply the reader with some information that becomes important to the resolution at the end of the story.
After we're done with Pat we come to the third big transition - into the fourth section. Again, three centered asterisks.
We move from Annie and Pat to Annie and Steven. We've been hearing about Steven all through the story, so his appearance is no surprise. We end the third section with anticipation of a dreaded moment ("So, I nervously passed the last few days until his return.") Then we begin the fourth section with some misdirection - and that's another method/technique for handling a transition. The first sentence in the fourth section is Steven saying, "Annie, what made you do it?" We know about Annie's infidelity and the idea is to propel the reader into the last section of the story by giving the reader the immediate impression that Steven is reacting to Annie's infidelity, and hopefully the reader thinks she's spilled the beans. We quickly find out that the exclamation is related to Annie getting the new bed. But the misdirection serves as a good kickoff.
I know this is a lot more than you were likely looking for, but the story illustrates there are a few ways to do transitions, and when to do them, and why.
All three transitions involve moving to a section of the story involving pairings of different characters: Section one Introduction and Annie and Bradley. Transition. Section two: Annie and Ginny. Transition. Section three: Annie and Pat. Transition. Section four: Annie and Steven.
And three different things to do to help the transition. Transition one - to a new and major character whose presence is foreshadowed in the first section. Transition two - to a new and minor character whose introduction is sudden and unexpected (and has the reader wondering for a while just who she is). Transition three - introducing a new major character we've been hearing about the whole story (and making his introduction one that misdirects the reader into thinking the crisis is immediately at hand when it isn't.)
Hope this is helpful.