Russian Qwerty Layout Download
Since no one has specifically explained how to get the Russian phonetic let me try:
After you follow the instructions from the first post by Pawan Dhondiyal and you have the Russian Language added go back to the Language Control Panel (you'll see it if you just hit the start/windows button and start typing 'language'.
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In there you will see the Russian language listed, Click on Options link to the right
How to Change Your Keyboard Layout in Windows 8 or 10 Windows 10 New Keyboard Options Available Keyboard language keeps changing in Windows 10. How to change keyboard layout in windows 7. Russian Phonetic Keyboard Support for Windows 10, 8, 7, Vista, and XP (download), Russian Fonts 32 and 64-bit, RuWriter. Transliterated layout. Russian Keyboard Labels. Order On-line. Keyboard Layout, Download, Size. Armenian Phonetic Keyboard Layout, kbdamph.zip, (270 kb). Georgian Phonetic Keyboard Layout, kbdgeph.zip, (265 kb). Russian Phonetic Keyboard Layout, kbdruph.zip, (265 kb).
Download Qwerty Keyboard
Under Input Method click Add an Input Method

Qwerty Layout Keyboard
In the list select Russian - Mnemonic and that is the key
That is the phonetic keyboard you've been looking for and it's a very good one like typing 'ya' will give you a 'я' etc. As a tip I also bring up the on-screen keyboard when I use it in case I have difficulty guessing the English equivalent (again hit the start key and start typing 'keyboard' and you will see it) sometimes when you switch it doesn't change the on-screen keyboard right away, click it somewhere or min/restore it and it will refresh.
Russian Phonetic Keyboard Layout Download
The name Mnemonic is what threw me off at first and I started with Bulgarian Phonetic but that one is missing some Russian letters and is just not as good as the Mnemonic one.
Enjoy :)