Fun fact: a not-so-long time ago, a bunch of English grammarians decided that Latin was the best language ever. They thought Latin was so cool, in fact, that they tried to make English more like it. To do this, they applied Latin grammar rules to English.
And so a bunch of weird, arbitrary grammar commandments like "thou shalt not split infinitives" and "thou shalt not end a sentence with a preposition" were born.
Well, we say that's silly. You can totally do both of those things in English. People do it all the time and nothing bad ever happens, right?
Right. But there are still academic standards to consider, so we'll give you some guidance on that. Academics tend to say it's okay to end a sentence with a preposition as long as it "goes" with the verb. To determine this, find the object of the preposition and reunite it with its preposition. It might be good to change question pronouns (who, what, where, when) to other non-question pronouns (they, that, there, then). If they make sense together, it's okay.
Here are some examples where reuniting the preposition with its intended object doesn't make sense:
Where did you put the paper at?
*At here. / Over here. / In here. / Under here.
Where has Timmy gone to?
*To here. / Over here. / In here. / Under here.
These are colloquial expressions—that is, many, many people speak like this, but it's not Standard American English, which is what you need to use in an academic setting.
Compare those sentences with these, which are okay:
Who are you going to give that giant lollipop to?
To her. / To him.
I wonder what they're talking about.
About this. / About that.
But as always, check with Teach first before you blame us on your next grammar quiz.
"Sweetheart, I'm totally paying attention to your exciting story about what happened at the bank, but I need to figure out where my phone is at."
The preposition at is completely unnecessary here. It had no business being in the sentence at all. Simply get rid of it and move on.
"I was on hold for so long that I forgot what I was even on the phone for."
This one could go either way. If you deleted the preposition for, it would make the sentence nonsensical. But, at the same time, you could just say "I forgot why I was even on the phone."
And that, Shmoopers, is an example of grammar being ambiguous. Who knew?