What is the best text-mode web browser?

There are many text web browsers, as there are many graphical web browsers, so it really depends on what you're looking for. lynx is a common slim choice, Elinks has many features. Both of these support other protocols, such as ftp and gopher (Elinks even supports bittorrent). Elinks may also be built with support for JavaScript, using Mozilla's former JavaScript implementation, Spidermonkey.

There is also w3m, which can also be used through Emacs.

If you want to try one at random, Wikipedia has a list of text based browsers.

How to install these has more to do with how your distribution manages packages than with the browsers themselves. Some of them are probably in the package repositories for your distribution.

As of November 2015, the actively maintained browsers are links and lynx. Many of the changes in both relate to TLS and security. Here is the current state of progress:

• links - 2.12 - 2015. (Changelog)
• lynx - unstable 2.8.9dev - 2015, stable 2.8.8 - 2014. (Changelog)
• elinks - unstable 0.12pre6 - 2012, stable 0.11.7 - 2009. (Changelog)
• w3m - 0.5.3 - 2011, 0.5.2 - 2007

I like links2, but primarily because it has a cool, lightweight 'graphical' mode. It's similar to just plain 'links', but you can invoke it with -g to get a display that renders images. It's very easily X-forwardable, too. But, when you don't want the HTML image rendering, it works just fine in the native ncurses interface as well.