Familiarize yourself with literature. Most people are required to read some standard classics in school, so if you skipped them in school, now might be the time to revisit those older classics.
Keep an eye on the publishing, not just bestsellers. Generally the most popular books available will not get you the title "well read." Instead, read book reviews and keep an eye out for notable fiction lists (New York Times or the New York Review of Books, for example) that lean towards the literary. These books often require more brain power to finish, but they also garner more respect for having read them.
Tailor your reading to your interests and specialties. If you want to be well read among a particular crowd of people like engineers, writers or economists, read specifically within the standards of your field. Being knowledgeable about a particular field of study or profession will certainly make you well read within those boundaries.
Read widely if you wish to be well read in the broadest sense. If you desire to be knowledgeable about a variety of fields and time periods, read broadly from different periods of time, literary movements and within varying fields like art, philosophy, drama and religion.
Consult the experts if you don't know where to begin. If you need specific instruction and titles, consult a book like Harold Bloom's "How to Read and Why" for a discussion of the act of reading as well as specific works.
Pay close attention to what you read because without being able to discuss it, hardly anyone will know you are well read. When you finish a book, consult author interviews or reviews about the work for extra insight.