Colleges teach courses in Native languages, but classes can be too expensive for many interested in these ancient tongues. Native American Languages are quickly becoming extinct even within their own tribes. In reaction, tribes are now developing new resources to teach people their languages in order to keep their heritages alive and rekindle their diminishing cultures. Opportunity to learn to speak a Native language without having to resort to costly classes has never been better.
Find websites online that are dedicated to teaching Native languages. Choose the language of a tribe located near you so you can take advantage of the full variety of resources and practical application opportunities available in your area. Multilingualbooks.com is a good source of free language guides. Find pages written in the native language and use them together with the guides to get a feel for how native speakers use the language.
Free Native American Lessons and Courses: http://www.multilingualbooks.com/freelessons-nativeamerican.html
Spend part of your learning time listening to audio-visual resources available online of the language you choose to get the feel for how the language sounds. Play them back and try to speak along with the speaker until you are able to mimic the speech, even if you don't understand the words. Getting the feel of how the language sounds and feels to speak will help you speak it more coherently.
Study language books and literature about the Native culture in general at your local library. Museums allow you to study the indigenous culture's history and help you understand cultural contexts of words and syntax that language books can't teach you. Museums dedicated to the people of the language you are studying may also have free programs available to help you learn.
Find a pen pal, once you have learned enough vocabulary and syntax to hold a rudimentary conversation in the language. Your pen pal will let you know when they do not understand you or when you have the wrong idea about a word or phrase. When able, use voice communications such as online audio chat to help you speak fluently as well as to write the language. The Language Exchange is an online program that will help pair you native speakers of the language you are learning.
My Language Exchange.com http://www.mylanguageexchange.com/HowTo.asp
Immerse yourself in the culture of the language. Remember that many of the resources you used to learn were written by people who know the Native language as a second language. Spend time at a reservation where you can speak the language with the people who use it in their daily lives. Volunteer at the Reservation offices to help on the reservation where you will use the language in the culture that created it. The following link gives you a map and links to find the tribes closest to you.