I like to take a few seconds to scan the puzzle and try to predict basic sentence elements. As mentioned by others, a common English sentence pattern is "a blankety-blank is," "There is/are" (if it's "are," the subject is automatically plural, which gives you your "s," if the word is regular). "The best/worst thing about blank is blank." I also look for if/then constructions, as well as either/or; neither/nor not only...but...
Punctuation gives you clues, too (except for poetry, where the punctuation is not necessarily regular). As mentioned by others, you would expect to see a conjunction such as "and," "but," "for," "nor," "yet" after a comma (unless it's a list of things, in which case you automatically know you have "and" before the last item listed. Obviously, a period signals the start of a new sentence, but so does a semi-colon (
and a comma plus conjunction. The punctuation tells you that you have a new subject and verb to find. English sentences are pretty regular about being in this form: subject + verb, and then any modifiers. And, obviously, if you have a sentence that is a question, you need to find how, what, when, where, why, ect. Sometimes if I'm stuck here, I will call the second letter "h" and see how it goes. Some of the hardest puzzles have no punctuation to guide you.
Proverbs almost never use the first person, so if you have a proverbial saying, a one-letter word is going to be "a." Proverbs also regularly use the "imperative" mood, which is used for commands: "don't do...", etc.
Sometimes if I'm stuck, I will call the most frequent letter "e:" sometimes you just have to make a guess, jump in, and see where your guess takes you.