First, there is no "each" and no "other." :) Well, we are seasoned Hebrew-learners already, we are not surprised, are we? ;)

So, what is there instead? Surprisingly, "one" and... no, not "two"! It's "one" and "second"! Not "one and two" and not "first and second", but mixed! "One and second"! :D

For example:
"It was so dark, that it was difficult to see each other" - הָיָה כָּל כָּךְ חָשׁוּךְ שֶׁהָיָה קָשֶׁה לִרְאוֹת אֶחָד אֶת הַשֵּׁנִי
Or
"It's good when people understand each other" - טוֹב כְּשֶׁאֲנָשִׁים מְבִינִים אֶחָד אֶת הַשֵּׁנִי
But that's not all there is to it! In the examples above the most "default" preposition את was used. However, sometimes when we use "each" and 'other" we need another preposition, like in "to agree with each other", for example*. Then, we must change the pattern and insert the preposition we need between the "one" and the "other" - - לְהַסְכִּים אֶחָד עִם הַשֵּׁנִי

You may say here - but how do I know which preposition goes there? It seems to be totally random! Let see...

* Mark the placement of this preposition! It goes between the two words!
(If we rewrite it literally it's not that strange, actually - "to agree one with the second" :) )