What is interesting about many of the stories of Sherlock Holmes is the way in which he spends a very long time interrogating the person who has come to see him at the beginning of the story before any action takes place. In a sense, then, the rising action of this short story occurs after Holmes has spoken to Helen Stoner, and includes a number of events. Firstly, the sudden appearance of Dr. Grimesby Roylott after the exit of Helen Stoner clearly signifies the beginning of the rising action. Note the way he is described:
So tall was he that his hat actually brushed the cross bar of the doorway, and his breadth seemed ot span it across from side to side. A large face, seared with a thousand wrinkles, burned yellow with the sun, and marked with every evil passion, was turned from one to teh other of us, while his deep-set, bile-shot eyes, and his high, thin, fleshless nose, gave him somewhat the resemblance to a fierce old bird of prey.
Clearly this is key in setting up the conflict between Holmes and Roylott, and then leads on to the visit that Holmes makes to Stoke Moran and his investigation of the rooms, and then his plan to swap rooms with Helen Stoner for that night. This of course leads to the climax of Roylott's attempt to kill Helen (as he thinks), and the way that Holmes sends the snake back to kill its master.