More often than not, students fall foul of the correct grammar usage of "at." Like other prepositions, the word is easily misused, which is why many English teachers try to clarify its correct grammar usage.
Indeed, what makes prepositions tricky is that more than one can seem to fit in a sentence but the wrong one can change its meaning. The best way to learn the correct usage of at is to pay attention to people speaking and to what you're reading, and then keep practicing. Once you retain that information you will always be able to use this preposition correctly.
If the word at isn't working as a connector, then it will most likely be working as an adverb. As such, rather than connect words it will modify one of the words in the sentence.
A preposition is a relationship word (hence a "connector"). It's the sort of word that can explain the place, time, or relationship of a sentence, and link the words together. In the case of at, this preposition is commonly used to express specific location (e.g., "Joe is waiting at home"), specific time (e.g., "The appointment is at 9 P.M."), or a specific point (e.g., "The progress meter is at 75 percent.").
Believe it or not, there are just two points to remember about the use of prepositions like at.
You need to choose the right preposition for each sentence, remember a preposition is a connector bringing the parts of the sentence together. A preposition like at is likely to follow certain words in order to make the relationship crystal clear between other words in the sentence (looking at, depends on, driving by).
Here's an example sentence:
In this example, you could only use the preposition at. Otherwise, the meaning of the sentence would be compromised and completely unclear. "I am looking from him" or "I am looking on him" would make no sense.
Next, consider how and where the preposition at is placed in a sentence, that is, a preposition must generally be followed by a noun or pronoun. The noun or pronoun counts as the object of the preposition. This can get a little tricky, but if you look at the above sentence again, you'll see what we mean:
The analysis would go like so: the preposition at is followed by the pronoun him.
Here are some more examples. Notice the points noted above in play. First, at is acting as a connector, drawing the subject/verb together with the direct object. Second, at is followed by a noun or pronoun, most likely the direct object.
No doubt, using at can be a bit of a challenge. When students get into the whole notion of subjects, verbs, and direct objects, there can be a bit of a breakdown in learning. If that seems to be the core of the problem, try reviewing these 20 rules of subject-verb agreement.
As long as you remember that the preposition is the link, the connector, or the relationship word that holds the sentence together and makes everything else clear, it will be slightly easier to digest the whole preposition lesson.
Then, once at is mastered, why not take a stab at two of its cousins: in and on. You'll find all the details in Prepositions: Correct Usage of In and On.