The coin tossing and the introduction of the Tragedians
There's actually quite a bit of anticipation in the play, but at the very start, it's pretty unclear where it's going. Ros and Guil, as they argue and banter about the coin, seem more or less at a loss for what to do or what their purpose will be. The Tragedians show up and give them something to do for a while, though their purpose doesn't actually narrow until Claudius asks them to track down Hamlet.
The mysterious messenger and the pact with Claudius
An initial sense of purpose seems to come to Ros and Guil when they remember that they were awoken by a messenger banging on their shutters who told them that they had important official business. However, neither of them can remember exactly what he asked them to do, and so the sense of purpose is vague enough as to be useless. They really get embroiled in the action when Claudius asks them to find out what is wrong with Hamlet, and they agree without so much as a second thought. This is when they get wrapped up in Hamlet's troubles and the problems at the court.
Unknown past and the dress rehearsal
In the end of the play, Guil actually wonders about this moment where things began to go wrong. He cannot place it, but he thinks that there must have been one, perhaps way back toward the beginning, where he and Ros could have escaped their situation. It is difficult to place the exact moment for Ros and Guil, but one key moment comes in Act Two when they watch the Tragedians' dress rehearsal. It is during the dress rehearsal that it becomes overwhelmingly clear (to the audience anyway) what is going to happen to Ros and Guil. The two are literally shown their futures acted about by the band and, by failing to recognize themselves, they become locked into their fate.
The boat, the letter, and Guil stabs the Player
By the time Ros and Guil are on the boat, it is clear that their fate is out of their hands – the boat's direction is set. We discuss this more in Symbols, Images, and Allegory section on "The Boat." The two instances where Guil and Ros act out the presentation of the letter also take on a nightmarish quality – first when they realize they are taking their friend to his death, and then when they realize that they are headed to their deaths. This all culminates in Guil's manic verbal attack on the Player and his attempt to kill him. It is the most active thing Guil does in the play, and it is in vain. It's much like the nightmares where there is something incredibly threatening around you and you try to run but can't move or try to shout, but can't. The Player's light-heartedness about it doesn't hide the fact that it is a paralyzing moment for Guil and a very chilling one for the audience.
Destruction or Death
When the stage goes dark, leaving just Ros and Guil, their fate is sealed. Instead of having an elaborate death on-stage, they both disappear, which is how Guil defines death earlier on in the play. It's unclear exactly what force brings about their deaths. In Hamlet, the two are presumably killed by the English king when he gets the letter. Here it's more of a metaphysical death – a transition to not-being, as Guil would say.