The best simulators for iOS and Android, in my opinion are Xcode and Andy, respectively.

For Xcode, get on your Mac and go to the Appstore and select Xcode. Do note that it is over 2GB in size. Once it is installed, launching the simulator is easy.

1. Launch Xcode from your Applications:
   
2. Use the menu to launch the iOS simulator by going to Xcode, Open Developer Tool, Simulator:
   
3. Once in the simulator, you can use the default simulator or use the simulator menu to pick a device:
   

For emulating Android with Andy, simply go to http://andyroid.net and download and install the app. You will have an Android OS virtually present on your machine and it comes with some free stuff!

Enjoy!