The new Android Studio incorporates very significant performance improvements for the AVDs (emulated devices).
But when you initially install the Android Studio (or, when you update to a new version, such as Android Studio 2.0, which was recently released), the most important performance feature (at least if running on a Windows PC) is turned off by default. This is the HAXM emulator accelerator.
Open the Android SDK from the studio by selecting its icon from the top of the display (near the right side of the icons there), then select the SDKTools tab, and then check the box for the Intel x86 Emulator Accelerator (HAXM installer), click OK. Follow instructions to install the accelerator.
Be sure to completely exit Android Studio after installing, and then go to your SDK folder (C:\users\username\AppData\Local\extras\intel\Hardware_Accelerated_Execution_Manager, if you accepted the defaults). In this directory Go to extras\intel\Hardware_Accelerated_Execution_Manager and run the file named "intelhaxm-android.exe".
Then, re-enter the Studio, before running the AVD again.
Also, I found that when I updated from Android Studio 1.5 to version 2.0, I had to create entirely new AVDs, because all of my old ones ran so slowly as to be unusable (e.g., they were still booting up after five minutes - I never got one to completely boot). As soon as I created new ones, they ran quite well.