Sign up for a Swahili class at a local college or community center that includes basic grammar and writing. Read textbook assignments and dedicate several hours per week to doing homework. Dedicate several hours per week to understanding parts of speech including noun classes, verb conjugation and adjectives. Join a study group, or form one of your own to discuss assignments. Ask your teacher for help or clarification about any grammatical rules that you do not understand.
Purchase a Swahili grammar book written for English speakers such as "Modern Swahili Grammar," or "Swahili--A Foundation for Speaking, Reading, and Writing." Read chapter introductions and complete written exercises several times per week. Look up words that you do not understand in your Swahili-English dictionary. Search for basic Swahili reading materials such as books and magazines available through university libraries to familiarize yourself with written Swahili.
Use free online materials such as the free Swahili Grammar on the Mwana Simba website. Read each chapter lesson and write out the examples. Complete the written exercises at the bottom of each chapter page. Write simple Swahili entries in a journal or blog several times per week to practice your grammar. Read Swahili language media such as online newspapers with the help of a dictionary or the Google Translate tool. This will allow you to familiarize yourself with written Swahili.