Memory works (to put it simply) in 3 stages: attention, encoding (storing/associating with other info), and retrieval (remembering)
To optimize the final stage, you have to optimize the first two stages. This means you have to pay attention to the material, and you have to encode it well. (Which I'll explain below.) Additionally, if you repeat the process, you reinforce it. By retrieving something, you start to pay attention to it again, and then you are able to re-encode it better than before.
To optimize encoding, remember GOAT ME.
G is generate and test. i.e., quiz yourself, or otherwise come up with the answers on your own without just reading them. Even if you get it wrong, it helps more than if you just read the answer off the bat, because you're forcing yourself to think more about it (why was it wrong?). Test yourself in a way that will resemble what you'll actually have to do during the real test. (e.g., if you have to write essays on the test, instead of just writing and memorizing bullet points, actually write an essay multiple times without cheating, review it, and repeat until you can write it without forgetting any important points.) Other effective ways of testing yourself are teaching the material to someone else and talking about it out loud to yourself.
O is organize. This reduces the load on your brain and helps create reminders just by coloring, position, or associations with nearby material. For instance, a time line helps remember that event A came before event B in history, not necessarily because you memorized the dates but because you organized the info so that event A was written earlier and you happen to remember that it was written earlier. The position of the information becomes meaningful. You can organize with outlines, pictures, color coding, related material, etc. My use of "GOAT ME" can be thought of as organization. Another fun example (chunking) is as follows. Which of these seems easier to memorize: "CIAFBIKGBCNNUSABBCUK" or "CIA FBI KGB CNN USA BBC UK"?
A is for avoid illusions of learning. There are two kinds of memory: familiarity/recognition and recall. Recall is what you want. That's where you can remember the information on your own, as you might be expected to do on a test. Recognition is where you can't think of it on your own but if you see it you suddenly remember it. That's not good. You won't necessarily see it on your test, so you won't get a blatant reminder of it. Avoid study methods that rely on recognition. Similarly, a major problem with rereading material is "fluency". The more you read it, the easier reading it becomes, and when it feels easier to read, you assume you have learned it. You have not. You've just become more skilled at reading it. Don't bother highlighting your textbook in the first go either. You feel like you're picking out the important parts of the chapter but you can't know what's really important until you've read the whole thing. And then all you're gonna do anyway is go back and reread all the highlights, and as we've established, rereading is useless. If instead you actually organize the highlights and quiz yourself on them, highlighting may be useful. For a similar reason, rewriting information is also not very helpful unless you use it as a method of quizzing.
T is take breaks. This is HUGE. If nothing else, walk away with just this tip. Your memory works best if you study in frequent, short sessions rather than one long cram session. You don't give your brain a chance to store the earlier info you studied, so it just slips out of your mind, and you'll have wasted your time studying it. So study for awhile, go do something else for a bit, and come back to it, and repeat. One of my students said she taped information in front of her toilet so whenever she went to pee or something she could study for just a couple minutes. It sounds strange but it's actually a great idea (I'd advise, in line with G and A that you tape questions in front of the toilet and tape answers elsewhere so you can quiz yourself.) Another important part of this is that you need to sleep to keep that info in your head. Even if you take regular breaks, an all nighter will do more harm than good. Your memories are stored more permanently after sleep. This is just how the brain works. You can even try to work naps into your study sessions. It's a break + sleep! [EDIT: I do not know how long breaks SHOULD be, but I believe this varies from person to person. Just try to study over the course of days instead of hours.]
M is match learning and testing conditions. This is based off the principle of encoding specificity, which states that, if you want to optimize memory, then the conditions surrounding encoding (e.g., where you are when you study, how tired you are when you study, etc.) should be the same as those surrounding retrieval (e.g., where you are when you're tested, how tired you are when you're tested, etc.). This is because the conditions themselves serve as reminders. (Have you ever walked into the kitchen for something, forgotten why you were there, and as soon as you return to the other room you suddenly remember why you went to the kitchen?) This includes your environment and your physiology, serving as reminders. Think about noise level, size of room, lighting, types of furniture, mood, intoxication, sitting position, and even the way you work with the material (remember G and A). Studies show that learning while drunk is best remembered while drunk again. Learning after exercising, also best remembered after exercising. The alternative to this is that you should study under MANY different conditions. This way, the information comes easily to you regardless of your surrounding conditions. Otherwise, the information will unfortunately be associated with the specific circumstances you studied under and will be difficult to remember in any other situation. If you want to remember this stuff outside of being tested in class, STUDY UNDER MANY CONDITIONS. Study in a noisy place AND a quiet place, with and without coffee, etc.
E is elaborate. Think deeply about the material and make other associations with it. At the most extreme, this can mean truly understanding the concept, why it works, how it relates to other concepts, and how it's applied. But on a simpler level, it can be the following: Does it remind you of something else? Can you make a song out of it? Can you visually imagine it? How does it apply to you or your life? Instead of taking the material at face value, do something with it. The reason this is important is because of reminders. Memory works by having a network of associations. One thing reminds you of another. If you've thought deeply about it, you've probably associated it with something else in memory, which can then serve as a reminder. You can think, "Oh yeah, this is the term that inspired me to draw that silly stick figure to represent it. And I remember what the drawing looked like so now I remember what the term means." Additionally, the quality of the memory will be better if you have elaborated on it. Elaboration allows for a lot of creativity and individuality among studiers. Choose whichever method of elaboration works for you. Maybe you enjoy making up songs, drawing doodles, creating stories, visually imagining it, relating it to yourself, or just pondering about it. If you're studying history, you might try to think about it visually, imagine what people would have said or looked like, watch them in your head doing their historical stuff, or maybe you'd like to draw a quick doodly comic about a particular event, or maybe you wanna think about why this even was significant, or how it relates to another historical event.
If I had to summarize this in fewer points:
Keep similar conditions during studying and testing. This includes environmental surroundings, mental and physiological state, the way you think about the material, and so on. But if you want to remember this outside of class, study in a VARIETY of conditions, so that you don't associate the material with any particular condition.
Study briefly and frequently, and sleep.
But one other good point I would add is this:
Take notes BEFORE class if possible, and add to them whenever necessary. Do this by reading the textbook chapters ahead of time (and take notes; refer to your syllabus to find out which chapter is next, if applicable) or see if your teacher posts Powerpoints online ahead of time. This way, you're not just frantically writing notes in class and you'll actually be able to more fully pay attention to what the teacher is saying (remember: attention is the first step of the memory process!). You may think you can pay attention to the professor as you're writing, but you are actually dividing your attention and hurting your memory.
EDIT: Whoa, thanks for all the comments, the gold, and the upcoming pizza(s)! I'm trying to get to those who've asked questions, but my inbox has exploded, so sorry if I take awhile! I will try to edit as people offer other good points, but I'm already super close to the character limit! Trying to cut it down now.