As a pedagogical demonstration of Twitter data analysis, a case study of HIV/AIDS-related tweets around World AIDS Day, 2014, was presented. This study examined if Twitter users from countries with various income levels responded differently to World AIDS Day. The performance of support vector machine (SVM) models as classifiers of relevant tweets was evaluated. A manual coding of 1,826 randomly sampled HIV/AIDS-related original tweets from November 30 through December 2, 2014 was completed. Logistic regression was applied to analyze the association between the World Bank-designated income level of users’ self-reported countries and Twitter contents. To identify the optimal SVM model, 1278 (70%) of the 1826 sampled tweets were randomly selected as the training set, and 548 (30%) served as the test set. Another 180 tweets were separately sampled and coded as the held-out dataset. Compared with tweets from low-income countries, tweets from the Organization for Economic Cooperation and Development countries had 60% lower odds to mention epidemiology (adjusted odds ratio, aOR = 0.404; 95% CI: 0.166, 0.981) and three times the odds to mention compassion/support (aOR = 3.080; 95% CI: 1.179, 8.047). Tweets from lower-middle-income countries had 79% lower odds than tweets from low-income countries to mention HIV-affected sub-populations (aOR = 0.213; 95% CI: 0.068, 0.664). The optimal SVM model was able to identify relevant tweets from the held-out dataset of 180 tweets with an accuracy (F1 score) of 0.72. This study demonstrated how students can be taught to analyze Twitter data using manual coding, regression models, and SVM models.