Decide which kind of Brazilian visa you need. Different types of visits require different types of visas. There are tourism visas, business/work visas, seminar/conference visas, educational/research visas and many others. The length of your stay will be different for each different type of visa, as will the requirements to get each visa. Be completely honest with your Brazilian consulate when you are telling them what your purpose for visit is. Ultimately, it won't be any easier to get a tourism visa than a work visa, and if you run into trouble in Brazil for any reason, you won't have any explaining to do about why you're there.
Get a passport. In order to obtain a Brazilian visa, you must have a valid United States passport. Getting a passport is easy and can be done at your local post office. You will need to fill out the paperwork either there or at home, pay the passport registration fee, present your valid driver's license and two passport pictures. It generally takes up to 2 months to receive your new passport in the mail.
Apply in person. Application for a tourist visa (the most common Brazilian visa offered) requires that you bring your passport. It must be valid for at least 6 months from the date you intend on entering Brazil. You must also bring, or fill out there, the Brazilian tourist visa application and one passport-style photo. You must also bring your trip itinerary, including where you are staying and proof of airline purchase (flight numbers and arrival/departure dates). You must also provide a money order, cashiers check or certified check for $130.
Apply by mail. Applicants applying by mail must also include a copy of proof of residence within the jurisdiction of the consulate for 12 months. This can be a copy of your utility bill, driver's license or voter registration.