Well, first of all, don't start with the hard ones.
My favorite thing to do is substitute "the" for each 3 letter word until one of them works. Plus, the classic patterns:
A = A or I
ABB = ALL or OFF
ABCDC = WHERE or THERE
ABCB = HERE
ABC'D = __N'T
ABAC'D = DIDN'T
ABCADB = PEOPLE
I find that just by starting off with those simple ones, you can get most cryptoquotes. If none of those are there, then it gets tricky.
*** SPOILERS COMING UP ***
The first one I posted, I have no idea how I got started. I stared at it for at least a total of 2-3 hours. I tried substituting stuff for KXXY and IR but that got me nowhere. I concluded with like 99% sureness that X was E, so I drew that in darkly. Then I looked at the two 4-letter words in the top line. After enough time, I actually realized that they were "HAVE MORE". I don't know how, it was a moment of clarity. From there, it was easy.
The second one I posted, I guess that YQ was OF and filled it in. From there, I had RYEA RFZ -> ?O??
. Then in another moment of clarity I got "MOST MEN". Again, this was after a ton of staring. After that, it fell into place.
On the third one I posted, I instantly recognized "PEOPLE". Once that was filled in, I had _OO. That was obviously TOO. TOO _E_ PEOPLE was pretty obvious, and everything else fell into place.
The reason I love doing these so much is getting the really tricky ones. I'll usually spend my whole bus ride staring at a tough one, or lie in bed going over things in my mind. When I get them, it feels so friggin' good!
Another structure I was stuck on was:
ABC DEC CFG. Basically, __C __C C__. I spent hours with that running through my mind. That was the only lead in the puzzle, the rest was tough. Eventually, I write "THE" in the last one, So I had, __T __T THE. After much pondering, I got "BUT NOT THE", and sure enough it was right.