I suggest you read Anna Schmidt's survey [1]. Typically you need some supervised text classification methods for this kinds of task. Any machine learning algorithms that can be used for classification can be tailored for such a task. Alternatively, you can read my work-in-process that covers literature from a wider context [2]

[1] Anna Schmidt and Michael Wiegand. 2017. A survey on hate speech detection using natural language processing. In Proceedings of the Fifth International Workshop on Natural Language Processing for Social Media. Association for Computational Linguistics, Valencia, Spain, pages 1–10.

[2] Article Hate Speech Detection: A Solved Problem? The Challenging Cas...