Anti-aliasing is when you smoothen a line that appears jagged, by adding intermediate colors (intermediate being 1 or more colors inbetween the line and the background's color). If you can see a jagged line, and it's considerably noticeable, anti-aliasing (AA for short) should be applied. Preserving line thickness should be a concern while using this technique, though.
Dithering is when you have two colors and you apply them to an area in a checker-like pattern (or some close variation of this) to create the impression of a third color (mostly used for color conservation). Similar to cross-hatching on physical/non-pixel media.
Regarding the size for a line to require anti-aliasing, i think it's more of an organic thing, if you can see something that looks too abrupt and spoils the effect you want, you go in and smooth it, regardless of it's size. Probably more related to contrast and palette choice than anything else.
I think there's a wiki in progress with most of these concepts explained, but i've never been able to find information there, i didn't find it very browsing-friendly so i don't recommend it.