Reading
When it comes to building vocabulary, nothing beats reading. Reading allows you to not only to come in contact with new words, but also to gain new knowledge. Reading almost anything will help, but for advanced vocabulary builders, I recommend at least high school level novels and articles.
Writing
I cannot stress enough the importance of writing. Writing allows you to be able to use your new vocabulary in a way that you need not improvise. In other words, if you are not very comfortable with a new vocabulary word, you can take awhile to think about how to use it in your written context.
Study vocabulary roots
Many words, especially big words, contain word roots that can help you decipher their meaning. For example, the word circumlocution contains two roots: circum which means around, and loqu which means talk. From these roots, we can figure out that circumlocution means to talk around, or evasive speech. Having a firm knowledge of the different word roots will help you greatly in building your vocabulary.
Surround yourself with good language
Talk to smart adults who have a wide range of knowledge. These people usually use high level vocabulary and you can pick up many words from them.
Use new vocabulary in daily conversation
This allows you to use new vocabulary in a improvising manner, which allows you to become more familiar with them. Try to use several vocabulary words in conversation everyday.
Keep a vocabulary notebook
Whenever you're reading, keep a notebook handy so you can jot down words that you do not know the meaning of, so you can look them up later.
Make flashcards and look through them everyday
Put the words that you have the most trouble with on flashcards and look through them everyday. This is an old memorizing tactic but it works.
Watch documentaries and news on television
Instead of mindless game shows and soap operas, watch informational television such as documentaries and news broadcasts because these programs usually employ sophisticated language.
Listen to National Public Radio
National Public Radio is a great station that offers news and cultural programming, and also uses sophisticated language. You can also listen to other such stations.
Set your homepage to BBC, MSN, or other news sites
Set your homepage to one of these news sites so you can read a news article everyday. These news articles usually contain high level vocabulary.