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If you can't then "simplified Swahili" is a really good book. Also I don't know which country you live in but I would bet good money there is a Swahili speaking community in your nearest city. One other thing though, try to find a Tanzanian. Kenyan Swahili is full of slang (Sheng) and Nairobi Swahili is godawful.
Simplified Swahili: http://www.amazon.com/Simplified-Swahili-Longman-Language-Text/dp/0582623588
I haven't studied Swahili in much depth, but I have done a fair amount of research into what resources are available. (My family speak Luganda and Swahili - I plan to pick up Swahili in a couple of years but want to spend another year or two on my Japanese.)
In addition to the Storybooks Canada website suggestion, I'd like to add that this website has some intermediate and advanced level reading/listening material with conversations to follow.
For vocabulary, This Anki deck also has a set of cards to help you get started and memorise some essential vocab and grammar points. This Anki deck has the answers to the first 10 exercises to the Simplified Swahili book which is often recommended as the must-have Swahili grammar textbook.
Langcorrect is a website where you practise your writing skills and get corrected by native speakers. However, Swahili is not the most popular language, so it may take a couple of weeks before you receive any corrections.
Additionally, If you are looking for a tutor, Italki have a fair selection of teachers at an affordable price.
I hope that's enough to get you started. Good luck.
I have found Simplified Swahili by Peter M. Wilson to be helpful for grammar and vocabulary. If you're in the U.S. it's fairly cheap on Amazon.
For Swahili there are quite a few resources, though Language Transfer and Simplified Swahili (grammar guide) are often recommended.
I dabbled a bit with Swahili but dropped it as I'm currently focusing on Japanese, though I may pick it up again in a few years. This website has some good simple stories with visual aids. This Anki deck has a set of cards to help you get started and memorise some essential vocab and grammar points.
Also, here is an Anki deck with the answers to the first 10 exercises to the Simplified Swahili book which is often recommended as the must have Swahili grammar textbook/reference guide.
While I agree that immersion plays an important role in language learning, I can't say that immersion alone is advisable for language learning, especially at a beginner level. Check out my thread here on my progress with Japanese, and this post for reference.