How do I become more detail-oriented and aware? I seem to always

Best advice I can give you: slow down. Mistakes like that happen when you're too confident so you go too fast. In that test situation, read the sentence word by word, following along with a pen or your finger and use a highlighter to mark the important terms.

Pretty much already been said, but slow the fuck down.
In your specific example you are focusing on the proposition, that is to say the cognitive meaning of the sentence, rather than the sentence's structure and word choice. This is a technique we naturally develop as readers to increase speed, but it can be very harmful when dealing with new material that may hold unexpected logical operators such as an and instead of an or, or a not before a phrase or term. You need to restrain these sanic speed instincts. You don't simply "become" more detail oriented or aware, you must constantly strive to pay attention to detail and remain ever vigilant. Think about what happens when you have to remember a person's name. You don't try to become better at remembering names, you try to remember that specific peraon's name. The majority of our actions are from a set of habits though, so by doing these things you do train yourself to do them in the future, but there is no golden process to hasten this conditioning.