when does one use "which" instead of "that" in a sentence?

Which is used for a non-restrictive clause that describes but does not limit the noun to which it refers. So if you are describing the crowd, use which with the commas. That is used in a restrictive clause, with no commas, to limit the noun to only one possible noun. For example, if I said "The horse that has brown spots is in the pasture," I am limiting the idea of "horse" to only the one with brown spots, as opposed to the other horses without the brown spots. If I said "The horse, which has brown spots, is in the pasture," I am merely describing the horse's appearance and not trying to differentiate it from any other possible horse.

That being said, I wouldn't use either! I would change your sentence to:

"The crowd, clamoring for the players to appear, was unusually rowdy..."

Hope that helps!

Oh, and check out the link for a more detailed explanation!

When one has already used "that" one would use "which" as "in I ate that which I preferred." Otherwise it's a matter of flow, the first sentence sounds too stodgy and is unnecessarily specific requiring the comma. Whereas the second example could be written without the first comma.

Both examples sound awkward to me and I would have gone with: "Clamoring to see their team, the ordinarily reserved crowd was unusually rowdy on this occasion..." although you described the rowdiness of the crowd twice in that example so perhaps the best way to say this would be: "In eager anticipation of their team's arrival, the normally sedate crowd was uncharacteristically rowdy tonight." "That" and "which" are often interchangeable as in this continuation of that thought: "And by the time the Moldavia Meercats finally did arrive, the rowdiness grew to a fervor (that or which) erupted into a full blown riot!

the first one is better. you could use the second one without the commas, but the first one as written is better.