Most good stories start with a fundamental list of ingredients: the initial situation, conflict, complication, climax, suspense, denouement, and conclusion. Great writers sometimes shake up the recipe and add some spice.
Since the play's two plots run parallel for most of the time, we'll identify each stage for each plot.
Initial Situation
Septimus's affair with Mrs. Chater is discovered / Bernard joins Hannah in research at Sidley Park
This is where we come in: a cast of characters worthy of a murder mystery is established at an English country house, ready for hijinks to ensue.
Conflict
Mr. Chater confronts Septimus about his affair with Mrs. Chater / Bernard and Hannah clash over Bernard's Byron theories
In the nineteenth-century stream of events, Mr. Chater wants to conflict – violently – with the man he thinks has seduced his wife. Over in the twentieth century, Bernard and Hannah's arguments over Bernard's theories demonstrate two contrasting ways of thinking about truth and proof.
Complication
After Septimus talks Mr. Chater down, Mr. Chater finds out from Byron that Septimus dissed his poem / Bernard finds some evidence to support his theory
Septimus thinks he's talked himself out of a duel, but he finds it tougher to wriggle out of the situation when Byron fingers him for Chater's bad press, especially since the less-easily-swayed Captain Brice takes Chater's side. And while Hannah thinks Bernard's crackpot theories are unprovable, he does manage to turn up enough evidence to convince himself, if not her, to stay on the trail.
Climax
Lady Croom sends away the Byron-Chater-Brice love polygon and discovers that she herself is the torch Septimus has been carrying / Bernard goes public with his theories
The night of reckoning, in which everyone's secrets come out, causes a giant shift not just in the sense of who stays and who goes, but also among . Once Bernard goes on television to promote his theories, there's no turning back: he's got to stand (or fall) by them, no matter what.
Suspense
Lady Croom finds another admirer, leaving Septimus in the cold / Hannah continues her research, knowing that something is going to prove Bernard wrong sooner or later, hopefully sooner
At this point, everyone (in both centuries) is in a holding pattern: Septimus obviously still has feelings for Lady Croom, even though her attentions have turned elsewhere, and Bernard is trying to stretch out his 15 minutes of fame as long as possible.
Denouement
There's something going on between Septimus and Thomasina that involves kissing and waltzing / Hannah discovers proof that Bernard is wrong
The kisses between Septimus and Thomasina seem innocent at first, but come to suggest something more – although the end of the play and the implied death of Thomasina prevent whatever it is (true love? Septimus finding another substitute for Lady Croom?) from developing very far. In any case, this a twist that suggests a possible conclusion to the suspense and sets up the conditions for the ending. Similarly, Hannah's discovery of the true fate of Mr. Chater brings about the end to Bernard's theories.
Conclusion
Everybody waltzes. The end.
Even though there are plenty of threads left untied at the end of the play, the concluding dance suggests that it's the process, the movement, that's more important than having all the facts wrapped up in a neat little package. (See "What's Up with the Ending?" for more.)