There is an abundance of free resources online for learning Mandarin, including dictionaries, grammar reference sites, podcasts, community forums and free university courses. Though these methods work in different ways, they can all help a person to different levels of Mandarin fluency.
Line Dictionary provides a definition for a word or character searched and gives a series of phrases to help give the word context within the definition. People can also try Pleco for smartphones, which is another useful dictionary that also works offline.
Chinese Grammar Wiki is a thorough wiki page for learning grammar, but for a more formal course, MIT offers a free online Mandarin class. The BBC also has an online course with excellent resources. Another helpful tool to keep track of everything learned is Anki, an online flashcard system.
It’s also important to hear and engage with real-world speakers when learning a new language. FluentU offers a collection of Mandarin YouTube videos with English subtitles. PopUp Chinese is a helpful resource of archived podcasts for learning Mandarin. CNTV, the Chinese News Network, streams news programs and other TV shows all in Mandarin. Furthermore, Chinese Forums is an established online community where learners can connect with native speakers, ask questions and generally engage in the culture.