Open the "Preferences" dialog in the Arduino IDE.
Click on the symbol next to "Additional Board Manager URLs"
Paste the following into the box (possibly on a new line under
any existing URLs), then click OK.
Note that you can click on the circled link for a list of
boards. This will open in your web browser. You may have to switch
to your browser to notice it.
Click OK to close the Preferences dialog box.
In the Tools menu/Board select the Boards Manager:
Scroll down until you see the Attiny entry (or the one for the
board you want), click on it to select it, and then click
Once done, close the Board Manager dialog box.
You should now be able to select Attiny from the Boards
Now in the Tools menu you can select which Attiny you want to
Notice you can also select the appropriate clock speed in an
adjacent menu item.
To program the Attiny you will need a suitable ISP (In System
Programmer) such as the AVRISP programmer, or the USBtinyISP