I recently upgrade from the 1.0.5 version of the Arduino IDE to 1.6.1. Things aren’t completely smooth - in particular, I was using Coding Badly’s cores for ATtiny85, ATtiny84 and ATtiny2313.
Unfortunately, those haven’t yet been updated for the new layout specified in the 1.6.x IDE. So instead I switched for now at least to the damellis cores (which support ATtiny85 and ATtiny84, but not ATtiny2313/4313).
Installing this is a matter of unzipping it in the sketchbook/hardware folder (on my Windows box in C:\Users\{my user}\Documents\Arduino).
In Windows cmd shell: cd "C:\Users\{my user}\Documents\Arduino" mkdir hardware unzip c:\{whatever}\attiny-ide-1.6.x.zip cd hardware move ..\attiny-ide-1.6.x\attiny . cd .. rmdir attiny-ide-1.6.x
At some point in the future either the Coding Badly cores will support IDE 1.6 (hopefully with the nice variants structure that the damellis cores use) or the damellis cores will do ATtinyX313s.