Under Construction
The most important way to increase vocabulary is certainly to read a lot. Most people don't remember a word the first time they read or hear it; one study says that we have to hear or read a new word at least eight times before we really remember it. So to increase your vocabulary, you should get a lot of "input" in English. Of course, do your reading homework for classes, but also try to read something in English for pleasure. Choose an easy book or a magazine on a topic you are interested, and read at least a little everyday while you are on the train or before you go to bed.
If you are the kind of person who learns by listening, you might want to get a book on CD or cassette. You can listen to the story first, and then read it again afterwards.
What should you do if you don't know the meaning? That depends on the time and place you are learning the word, and how important the word is. You can't look up every word you don't know in the dictionary. If you did that, you wouldn't be able to read or listen to very much English.
When you are reading, you may find that you can actually guess the meanings of some words from the context. When I am reading something in Japanese, I usually try to read a big chunk (a few pages or more) without using a dictionary at all, just getting the main idea. Then I read again more slowly. On the second reading, I can guess the meanings of many of the words. (If I am at home and I have a lot of time, I sometimes check in a dictionary to make sure, but if I'm reading on a a train, for example, I don't check the meanings if I can guess.) There may still be some words that I don't understand and which seem very important--as when the same word is found several times on the page, and it seems that I can't understand without knowing that word. In that case. I look up the word in the dictionary.
After you look it up, there are different techniques for remembering words. For example, some people write down those words so that they can try to memorize them. If you have an electronic dictionary, sometimes you can store the words you look up and quiz yourself later.
When you are reading for your classes, you need to make sure you understand the key terms in the lectures and readings. Usually, you'll be able to identify the key terms--the textbook will define or explain them, or the teacher will define them or point them out in some way. In the case of these words, you want to be sure to memorize them.
Some people also find that it helps to buy workbooks for practicing vocabulary. For example, there are books which can help you increase your vocabulary to prepare for the TOEFL test. There are books like this for Japanese too, but I don't like using them--I get bored quickly. But if you like that kind of book, I think it can be very helpful for increasing your vocabulary. You can find some at any bookstore that has lots of books for English study.
Finally, there are lots of web sites. Some of them actually want you to pay, but there are other sites with free information, games, or quizzes. Here are just a few.