You begin your SiSwati study by learning some basic phrases and vocabulary. The website "SA Languages" features a section on SiSwati, including a page on "General Words and Phrases". It's a good beginner's introduction to conversational essentials. Here you can learn greetings, useful words like "please," "thank you" and "emergency," and simple yet helpful questions you can use every day such as "How much is this?" and "What is the time?" You can also familiarize yourself with beginning numbers.
The Peace Corps has also put online a manual for learning basic SiSwati. It covers pronunciation and greetings, but also delves into more conversational elements, such as how to say, "Good morning," "How are you?" and "Pleased to meet you." There are sections on health vocabulary, identifying family members, naming different kinds of food, directions and finding your way around and time. The Peace Corps manual also gives information about the history of SiSwati and language-oriented cultural notes.
SA Languages also has a SiSwati texts page for your to practice your reading. Though SiSwati is spelled with the same letters as English, reading in it can take some getting used to. The Texts page has two short passages: The Lord's Prayer in both SiSwati and English, and a short reading about the National Language Service.
Once you have learned a little SiSwati, you will probably be eager to try it out. People learn languages more thoroughly and fluently when they practice them in a natural context, so if you don't live in a place with a community of people who know Swati, you may be interested in joining a language exchange. Language exchanges on the Internet usually function as linguistic matchmakers. You can look at a list of people who are interested in learning English and are willing to practice their language, this case Swati, with you in exchange. You can usually send messages through the website after you've registered to avoid having to give out your personal email if you so desire.