To type in Russian (both in KOI8-R and CP-1251) in the Windows 3.x applications, I use a nice free keyboard program WinKey (author - Gavin Helf).
It works both in Windows 3.x and Windows 95/98 (though I heard that sometimes it has a minor interface problems under Windows 95).
It does not work in Windows NT/2000.

This page explains how to use CP-1251 Russian keyboard with WinKey.
KOI8-R keyboard with WinKey is explained on the page
"KOI8-R Keyboard: standard and phonetic layouts".

Installation and setup of WinKey is described in details on this site's page "Russian in Browsers/Mail/News under Windows". Read there about WinKey - go to a section devoted to Netscape ver. 1,2,3,4 and there, in Chapter 6 of this Netscape-related page, find WinKey instructions (in English or in Russian).

The picture of my phonetic (transliterated) layout was given in the 'parent' page - "Russian Keyboard: Standard and Phonetic Layouts" section of my site, but I'll repeat it here, too:

Some letters are assigned to the combination of the keys:
rarely used letter 'yo': and letter 'hard-sign': to the following key combinations (with Ctrl-Alt pressed - it's the same as this special AltGr button that is present on some European keyboards):

I created my CP-1251 phonetic layout file for WinKey program, too:

y1251.wkb - to type using CP-1251(win) fonts

You may download this file - it's here, inside KBD31-Y.zip file-archive. Just click on this underlined file name and your Web browser will offer you to Save File on your PC. Put the file into some directory(folder), say, C:\RUS-Y. NOTE: If the browser instead begins to display the contents of this file on the screen, then try to download it again, but this time hold down the SHIFT key on your keyboard while clicking on that file.

After downloading the archive (.zip file), you need to open (unzip) it to extract the files in it.
You can extract files from the archive using the shareware program WinZip for Windows OR simply with the small free MS DOS program pkunzip.
If you don't have PKUNZIP, you can download it here: pkunzip.exe.
Put it into the folder where your have your Windows system files, that is, into the main MS Windows directory(folder).

To extract files from the archive using pkunzip program, open an MS-DOS window first (it's an icon "MS-DOS Prompt" in the Main group) and then type two MS DOS commands (the first one switches to the required directory (folder) and the second one does the extraction):

       C:\.....> cd \RUS-Y
       C:\RUS-Y> pkunzip KBD31-Y.zip

After extracting files from KBD31-Y.zip archive, you need to copy them into KEYBOARD sub-directory of C:\WINKEY directory.

To use my Layouts in WinKey, do the following (as was explained above, WinKey switches a keyboard - using a ScrollLock button - from English to an Alternate layout which will be one of Russian layouts here):  

1. Open WinKey application
2. Click once on WinKey icon (it has a Flag on it)
   
   • Windows 3.1 - click with Left mouse button
   • Windows 95/98/ME - click with Right mouse button
   
   
3. Select Menu Configure option

4. Click on available Alternate 5 button in the right column
5. Input corresponding information for my CP-1251 Layout:
   • Menu Name - up to you, f.e. YaWERT 1251
   • Select Russia in Icon list
   • Select file y1251.wkb in Keyboard File list
   
   
6. Click on Save button on the right

1. Select Alternate Keyboard option
   and then
2. Select YaWERT 1251

Important!
If you want to use one Russian layout most of the time, for example, use Scroll Lock to switch between English and my 'phonetic' CP-1251 layout, then you should make it Item no. 1 in WinKey's Alternate Keyboard menu.
Then you will not need to go to WinKey menu each time you call this program, because by default WinKey switches between English and "Alternate 1":

• click once on WinKey's icon and select an item Menu Configure
• look what settings are made currently for "Alternate 1" and write them down on a piece of paper
• then install your preferred layout as "Alternate 1" by following the steps described above for "Alternate 5"
• If you want to keep former Item no. 1 layout, install it where you had your preferred layout before (for example, as "Alternate 5")

Reminder: to be able to type in Russian, you need to do TWO things:

• select corresponding Russian font (CP-1251 in this case)
• switch your keyboard into the corresponding mode using WinKey (CP-1251 mode in this case)

To return, click on the Back button of your browser.

Information provided by Paul Gorodyansky
(author of the site "Cyrillic(Russian): instructions for Windows and Internet")