With only the King left, how can you get a draw? Let's say I have only the King left.

I've read several rules and posts of people saying there is a limit to the number of moves your opponent has to check mate you in, but there are some inconsistencies:


I found the number of moves varying depending on where I found the info. It seems to be 50, but I am not 100% sure.
It seems there are some exceptions and cases where the count is reset, but the information seems quite spread all over.


I'd like to understand this rule in detail and know all the special cases if possible, as it seems way too fuzzy for me and the people I play with.
If a player has a theoretical win, that person has a move limit (50 moves) with "no fundamental alteration of the position." That means no captures of pawns or pieces, and no pawn moves. The count is reset if either of these things happens.

There used to be an  exception for positions like king, bishop, and knight vs. King (a checkmate). It was known to be winnable in a maximum of 34 moves. But players got twice this maximum, or 68 moves (Milton Hanauer, "Chess Made Simple"). Apparently, this, and other exceptions, were removed later, according to a comment below.