Grab the update here: http://getk2.org/downloads/?f=K2_v2.6.1.zip
If you are on Joomla! 1.5, grab the zip file from the link above and install it on top of your existing K2 version. If you are on Joomla! 2.5 or 3.0, go to the Joomla! update manager, purge the update cache, re-check and you'll see the new release available to instantly update. If you are on Joomla! 1.6 or 1.7 then someone probably cut off your internet connection a year ago: upgrade to 2.5 now!!
However, there are 2 important changes that you need to be aware of:
1. The module mod_k2_login has been completely dropped from the K2 package. Use mod_k2_user instead. If you upgrade to K2 v2.6.1, you're mod_k2_login module will simply not work. So if you haven't already, do the switch now to mod_k2_user. If you don't want digital garbage left behind, feel free to uninstall mod_k2_login. Anything you do, BACKUP FIRST!
2. All "user" related template override files (2 inside components/com_k2/templates called register.php and profile.php and another 2 in /modules/mod_k2_user/tmpl/) have been updated since 2.6.0 and simplified in 2.6.1 to avoid Joomla! specific input form rendering. We previously used a PHP constant to determine whether we were gonna render input fields the Joomla! 1.5 or 1.6+ way. This is basically what happens when the Joomla! API constantly changes, but that's another story to tell... So because of that, you NEED TO UPDATE all these 4 overrides. We will be providing template overriding packages so you can use a program like WinMerge (Windows) or FileMerge (Mac) to determine the exact changes and apply them to your overrides in your site. If you don't use any overrides for these files, then you don't need to do anything obviously.
If you do this work now and upgrade to 2.6.1, any update following (2.6.2 etc.) will be painless.
In the future we'll be more careful to decouple such PHP/Joomla! API logic from template overrides and provide them "as clean as possible", so they are future-proof.
We're also aware of a few "setup" glitches, mainly that the backend dashboard modules are not setup there after K2 is installed or upgraded in Joomla! 3.0. You can go ahead and publish them on your own in the "cpanel" position via the module manager for "administrator" modules.
Update: We have now updated the K2 template overrides page. You'll see that the only changes between v2.6.0 and 2.6.1 are reflected in the 4 overrides we mentioned earlier.