The hardest part of self-editing is knowing when you're doing something wrong if you don't actually know you're doing something wrong. You might have an inkling and check a reputable source and figure out how to fix your sentence or story, but, other times, you might think you know what you're doing yet still get it wrong. But sometimes we're taught wrong. I think many older authors will recognize these grammar don't rules that are really grammar do rules!

Ending a Sentence with a Preposition
First off a preposition is a word that relates time, place, or direction. Basically, everyone knows preposition words like on, over, down, up, but let’s give some examples of each of the basic prepositions you’ll commonly find or use.

For Example:
Prepositions with Place: These words link the noun with a particular spot, indicating location or position.
Near: He parked near my car in the lot.
Off: The cat jumped off the counter.
Behind: The extinguisher is behind the door.

Prepositions with Time: These words tell us when something is happening.
On: We play jokes on April Fool’s Day.
At: Dinner is at six.
In: Christmas is in December.

Prepositions with Direction: These relate to movement of the subject.
Over: We flew over the mountains.
To: We drove to the party.
Across: The ball bounced across the floor.

Now, you’ll notice that none of those sentences end with a preposition. But plenty of times a sentence can end with a preposition and still be correct. The myth that it is “proper English” not to do so comes from severely outdated rules that apply to Latin contructs. Well… we don’t speak Latin anymore, and the English language is constantly evolving. It is unnecessary formal to always bury the preposition inside a sentence.

For example:

The little boy had no one to play with vs. The little boy had no one with whom to play.
Who were you talking to? vs. To whom were you talking?
There’s nothing to be scared of vs. There’s nothing of which to be scared.

Which would you use? Which sounds more natural? Of course, most of the time you can find a way to place the preposition within the sentence, but if you can’t, don’t worry about it! Go ahead and drop it at the end of a sentence and move on!

Beginning a Sentence with a Conjunction
I bet students who had this rule drummed into them as kids caught my gaffe earlier in this post where I used ‘But’ to begin a sentence. It wasn’t a mistake though, because it isn't actually improper grammar. This is something that I was corrected on and smacked hands over a few years back before I learned better. Let's see how authors have been ignoring this so-called ‘rule’ for forever.

For Example:

In a Romeo and Juliet the play begins with two Capulet men having a discussion in Verona where this so called ‘rule’ is ignored:
Sampson says, “I strike quickly, being moved.”
Gregory says, “But thou are not quickly moved to strike.”

The first pages of The Adventures of Huckleberry Finn has:
I got into my old rags and my sugar-hogshead again, and was free and satisfied. But Tom Sawyer he hunted me up and said he was going to start a band of robbers, and I might join if I would go back to the widow and be respectable. So I went back.

Tolkien’s Lord of the Rings Book One Prologue has this passage in the prologue:
They are possessed from the first the art of disappearing swiftly and silently, when large folk whom they do not wish to meet come blundering by; and this art they have developed until to Men it may seem magical. But hobbits have not, in fact, studied magic of any kind, and their elusiveness is due solely to a professional skill that hereditary and practice, and a close friendship with the earth, have rendered inimitable by bigger and clumsier races.

Chapter One of The Hunger Games by Suzanne Collins uses:
The last thing I needed was another mouth to feed. But Prim begged so hard, cried even, that I had to let him stay.

So if you feel like starting a sentence with and, but, for… feel free!