type RUSSIANEASY on Latin keyboard (IME)

http://RUSSIANEASY.NET
for more information

Use English/Western/Latin keyboard to type Russian/Cyrillic.

type Russian with the RUSSIANEASY map, use F4 to toggle it ON/OFF in text boxes

a а b б v в g г d д e е ó/yo/ö ё w ж z з i и j й
k к l л m м n н o о p п r р s с t т u у f ф
x х ç/cz ц c ч h ш ý/yy щ º/'' ъ y ы ' ь é/ey/ä э ú/yu/ü ю q/ya я

switch captions (CC) on in video to see an example of the mapping.

for pages with many textboxes on FIREFOX, use this add-on to activate in whole page, instructions on RUSSIANEASY.NET:
https://addons.mozilla.org/en-US/firefox/addon/transliterator/