Google Webmaster Tools blog just published a video to help learn more about the rel="next" and rel="prev" for paginated content. "Paginated content includes things like an article that spans several URLs/pages, or an e-commerce product category that spans multiple pages."
"Remember that if you have paginated content, it's fine to leave it as-is and not add rel="next" and rel="prev" markup at all. But if you're interested in pagination markup as a strong hint for us to better understand your site, we hope these resources help answer your questions! With rel="next" and rel="prev" markup, you can provide a strong hint to Google that you would like us to treat these pages as a logical sequence, thus consolidating their linking properties and usually sending searchers to the first page," blogged Maile Ohye, Developer Programs Tech Lead.
Does rel=next/prev also work as a signal for only one page of the series (page 1 in most cases?) to be included in the search index? Or would noindex tags need to be present on page 2 and on?
"When you implement rel="next" and rel="prev" on component pages of a series, we'll then consolidate the indexing properties from the component pages and attempt to direct users to the most relevant page/URL. This is typically the first page. There's no need to mark page 2 to n of the series with noindex unless you're sure that you don't want those pages to appear in search results," explains Google.
Should I use the rel next/prev into [sic] the section of a blog even if the two contents are not strictly correlated (but they are just time-sequential)?
"In regard to using rel="next" and rel="prev" for entries in your blog that "are not strictly correlated (but they are just time-sequential)," pagination markup likely isn't the best use of your time -- time-sequential pages aren't nearly as helpful to our indexing process as semantically related content, such as pagination on component pages in an article or category. It's fine if you include the markup on your time-sequential pages, but please note that it's not the most helpful use case," Google said.
The following video /slide on pagination covers the basics of rel="next" and rel="prev" and how it could be useful for your site:
You can also refer the followning Webmaster Help Center article with more implementations of rel="next" and rel="prev", and this Webmaster Forum thread with in-depth answers to the community's questions on the topic.