Question about the order of posts

When searching a particular tag, are posts arranged from newest to oldest?

By default yes.

Because I don't know how, what are the other ways to order posts, and where are they listed on-site?

From the Cheat Sheet :

• order:id Order search results in ascending order based on post ID.
• order:id_desc Order search results in descending order based on post ID. * this is the default *
• order:score Order search results in descending order based on post score.
• order:score_asc Order search results in ascending order based on post score.
• order:mpixels Order search results in descending order based on resolution.
• order:mpixels_asc Order search results in descending order based on resolution.
• order:filesize Order search results in descending order based on file size.
• order:landscape Order landscape images first.
• order:portrait Order portrait images first.
• order:favcount Order search results in descending order based on number of favorites.

Thank you kindly. Would you happen to know if there's been request for a random order...meta-tag(?)?
EDIT: Oh, or by "number of tags", which I'd imagine would be useful for bored taggers)?

I couldn't say for sure, but I think I saw something like that on the trac, but it's down ATM, so I can't check. It may have been nixed if it was there.

T5J8F8 said:
Thank you kindly. Would you happen to know if there's been request for a random order...meta-tag(?)?

There is; I made the trac for it a while back. Not nixed, I think, just ignored.

Not just on the trac, I think people have requested it in the forum at least twice in recent memory.