The most common IDE (99% use it) is Eclipse Pulsar IDE.
You can downloadwebpage For the SDK, obviously the Android SDK which is available webpage.
After downloading the SDK you have to unzip it and the SDK will install all its components automatically.
But you also neet a plugin called "ADT-Plugin" which is installed in the eclipse IDE. I was not able to find any links to it so you can google and find your way.
To run the app on your mobile first install the driver of your phone on your computer then connect you phone to the computer through a USB cable then, from eclipse, on the left pane, right click on the project name and click on run. The app will automatically start running on your phone