While College Board's classification doesn't get more specific than "Words in Context", there are actually two distinct types of "Words in Context" questions that you might encounter. In one, they leave a word blank and ask you to pick the most appropriate word to fill in the blank. In the other, they underline a word and ask you to pick the word that is closest to the definition of that word as it is used in the context of the passage. Here we are covering the first type.
You will know that you are looking at a one of these questions because the question is always worded exactly the same. It will say "Which choice completes the text with the most logical and precise word or phrase?" Plus, you'll see a blank space where the word should go in the question.
As always with Reading & Writing questions, you should start by reading the question. This tells us what type of question we're dealing with. Then, go back and read the passage, making sure to comprehend the passage as a whole, and what you think it is trying to say. Then, before looking at the answer choices, try to think of a word in your head that would make sense to fill in the blank. It can even be a few words, but something that conveys the meaning of what you think should go in the blank. Next, look at the answer choices and see if any of them match what you thought of. If you see a word that matches what you thought of, or is a close synonym, then you can be pretty confident that you've got the right answer. If not, then try inserting the answers one by one in the blank, and seeing if the passage makes sense with that word.
If you don't know the meaning of all the answer choices, then start with the ones you do know. If any don't seem like a good fit, then eliminate them. Just make sure you are somewhat open-minded to the possibility that words you do know might be used in different ways than you are used to seeing. If the process of elimination leaves you with just the word you don't know, then even though it's scary to pick a word you don't know, you should pick that one. If there are multiple words you don't know, then look for clues in the words as to what they might mean. Do you recognize roots, prefixes, or suffixes? Is it kind of similar to a word that you do know? For example, let's say you don't know what "proponent" means. It sounds pretty similar to "opponent", so they might be related. You might know that the prefix "pro-" means "for" or "in favor of", so whereas an opponent is someone against something, maybe a proponent is someone for something - and you would be right!
Keep in mind that College Board calls these questions "Words in Context" for a reason. The definition of a word can sometimes change depending on the context in which it's used. You might be familiar with using a certain word in a specific context, but not know how to interpret that word in a different context. For example, you might be familiar with the term "peripheral vision", and have an idea of what it means, but aren't familiar with how peripheral is used in other contexts. Try to use logic to infer - if peripheral vision refers to what is toward the edge of your field of vision, then maybe peripheral is a word that means "toward the edge of something", or "far from the center", or something along those lines. So keep an open mind that words you are somewhat familiar with might be correctly used in a way you aren't used to seeing.
In order to properly infer what would make proper sense in the blank, it's crucial that you properly interpret what the passage is trying to convey. Look out for clues that indicate the direction they are going with their statement, claim, argument, etc. Keeping an eye out for transition words and phrases can be very helpful. If we see a contrast transition word/phrase like "however", "nevertheless", or "on the other hand", then we know that the author is going to say something different than what they just said, which can inform what should go in the blank. If, on the other hand (see what I did there - transition phrase), we see a transition word like "likewise" or "furthermore", then we know that the author is going to say something more in agreement with what they just said, which can also inform what should go in the blank. Another good indicator is a colon, which indicates that the author is going to say something more about what they just said.