Interested in some informed speculation on how many links are needed, whether some are more prestigious than others, how long it typically takes to earn a full chain etc.
How long it typically takes to earn a full chain...
The most obvious canon quotes are from "A Feast for Crows";
and "A Game of Thrones";
In order to earn sufficient links to call oneself a 'Maester', it seems likely that you would need to study as an apprentice for around 10 years but potentially up to 20 before you are awarded the title. This is borne out by the advanced ages of the vast majority of Maesters seen as well as our own contemporary understanding of the time needed to achieve multiple doctorates.
How many links are needed...
From the TV series, we can see that the chains seem to contain approximately 20 links and from a quote from GRRM we know that Maesters can be awarded multiple links of the same metal if they are especially proficient in a particular area of knowledge. This suggests that a Maester never finishes learning or earning links.
Certain links, such as ravenry can only be awarded by an "Archmaster" whereas other links can be granted by the mutual assent of other Maesters or presumably even be self-awarded.
Whether some are more prestigious than others...
Some links such as Black Steel (Ravenry), Copper (History), Silver (Medicine), Pewter (unknown) and Bronze (Astronomy) seem common and relatively easy to attain since they're held by first and second-year students. Others such as Gold (Economics), Iron (Warfare) and Electrum (unknown) are particularly rare and seem to mark the passage into becoming a full-fledged Maester.
Valyrian Steel links (for the study of Magic + the Occult) are exceedingly rare and held by less than one Maester in a hundred. Ironically, they aren't seen as especially prestigious but rather viewed with suspicion.
Presumably it would take a few years, although I do not recall a specific time being mentioned at any point in the series. The actual length of time seems to depend upon each individual student.
For what it's worth, it is mentioned in the AFFC Prologue that Pate has been at the Citadel for five years but has failed to earn a link. On the other hand, Alleras has been there for a year and has already forged three links.
I'd imagine that the chain is somewhat similar to the 'badges' that scouts earn. Once you master one thing, you get the link which signifies that you're (at least) competent in that area. I'd also speculate that maesters never really finish adding links . . .