How did Holmes identify Stapleton as the criminal in Hound of the Baskervilles?

Sherlock Holmes initially began to suspect that Stapleton was behind the criminal dealings concerning the Baskerville estate when he closely examined the cryptic warning note received by Sir Henry.  While making a close inspection for the water-mark, Holmes held the paper "within a few inches of (his)eyes", and in doing so, became conscious of "a faint smell of the scent known as white jessamine".  The scent of perfume indicated the presence of a lady, which turned his attention to the Stapletons, since Beryl Stapleton was one of the few women living in the vicinity on the moor and the only one so far closely related to the case.

Upon looking into Stapleton's history, Holmes discovered a number of startling facts.  First of all, although Stapleton had presented Beryl as his sister, Holmes discovered that she was in fact his wife.  The fact that Stapleton was lying about this particular detail indicated some sort of sinister intent.  The big breakthrough for Holmes, however, was in uncovering Stapleton's true identity and his familial connection to the Baskervilles.  After noting an uncanny resemblance between Stapleton and a portrait of one of the Baskerville ancestors, Holmes inquired further and found that Stapleton was "the son of...Rodger Baskerville, the younger brother of Sir Charles, who fled with a sinister reputation to South America, where he was said to have died unmarried...(Rodger) did, as a matter of fact, marry, and had one child", the man who presently was calling himself Stapleton. 

As the son of Rodger Baskerville, there were "only two lives interven(ing) between (Stapleton) and a valuable estate".  With this information, Holmes knew that Stapleton, who was already acting with duplicity, had a strong motive for wanting Sir Charles and Sir Henry dead (Chapter 15).

What did Watson infer about Stapleton after their first encounter in The Hound of the Baskervilles?

Watson was able to infer from looking at Stapleton that he was the naturalist that had been spoken of.  Watson did this by noticing the things Stapleton had with him:  "A tin box for botanical specimens hung over his shoulder and he carried a green butterfly-net in one of his hands."

Watson also noticed that Stapleton had an unusual energy and manner about him.  Here is the description Watson gives of watching Stapleton run across the moor:   

 "...in an instant Stapleton was rushing with extraordinary energy and speed in pursuit of it. To my dismay the creature flew straight for the great mire, and my acquaintance never paused for an instant, bounding from tuft to tuft behind it, his green net waving in the air. His gray clothes and jerky, zigzag, irregular progress made him not unlike some huge moth himself."

While Watson will leave the Stapletons with nothing but a sense of concern for how isolated they are, this description, combined with Stapleton's questions, will begin to plant seeds of suspicion later on.