For this answer, as well as a few others, I've used quotes from the SRD as a source. How should I cite those properly, to help back up my claims, and prove that I'm not pulling quotes from my bum?
I generally use a link followed by a blockquote, if the quoted text is central to the answer, or just a link if it's a less central example.
So, to steal from your answer, I would say:
That action can be used only to take the Attack (one weapon attack only), Dash, Disengage, Hide, or Use an Object action.
(This is identical to what's in your answer, except that I made the word "Haste" into a hyperlink to the SRD entry you're quoting from.)
But if Haste were just an example, my answer might say:
You should try using buff spells (e.g., Haste) to help your party.
...without the blockquote.
I'll assume you intend to quote directly from the WotC document and not through a website's transcription. If you give the page number that helps, but if you want to link directly to a specific page in the SRD you can add a hash #page=num to your link.
For example if I want to reference the Grappler feat that is included in the SRD I could write my link like this:
[Grappler](http://media.wizards.com/2016/downloads/DND/SRD-OGL_V5.1.pdf#page=75 "D&D 5e SRD p.75")
Then if I want to quote from it I'd use a blockquote and copy+paste. Like so:
The Grappler feat (SRD p. 75) says in part:
You have advantage on attack rolls against a
creature you are grappling.
You could also link the page reference if you prefer. The Grappler feat (SRD p. 75) says in part:
You can use your action to try to pin a creature
grappled by you. To do so, make another grapple
check. If you succeed, you and the creature are
both restrained until the grapple ends.
Or use an inline link for more informal references.