I suspect this will depend somewhat on your level of knowledge in those other languages. Japanese is broadly considered a very difficult language for native English speakers, and it's pretty substantially different in many ways from English. Learning it is indeed possible, but takes a long time and a substantial commitment of energy. However, those with a decent fluency in Chinese (I use this rather than Cantonese/Mandarin because I don't understand the nuances well enough to speak intelligently as to their relation to Japanese-learning) or Korean (and probably many other languages) will have a much easier time with the transition compared to those with a primarily-English background. Additionally, Japanese Kanji have a relationship with Chinese characters, and so learning the Kanji is easier for one with a meaningful Chinese background who has had to learn those characters already.

For some context, one can attend Language School in Japan, which is a half-time (~20-25hr/wk) course load taught with full immersion learning. That is to say, the course is taught almost entirely in Japanese itself, but doesn't require any knowledge of the language to participate, as you'll work up from a near-zero understanding. In many of these classes, the first few weeks might lean a small amount on English to explain certain concepts, but the complexity of English required is very low. It takes about 2 years of these courses in order to reach a "basic" fluency. Many who take the 2-year course take the JLPT (Japanese-Language Proficiency Test) and study up for the exam can test into the N2 category, which is what you'd minimally need in order to attend school or seek a job in Japan.

Learning on your own, I'd probably say you should expect either to spend many hours a day on study, and/or to spend multiple years before you'd reach the point of being able to understand a significant amount of the anime you consume. Learning the grammar and vocabulary are one thing, but actually consuming content in the language is an important part of learning, and jumping from nothing to full-on anime is a HELL of a jump in complexity.

As to how to go about it, there are tons of excellent resources available online for paths to take. Most will point you to various textbooks to work through, which is a pretty decent strategy IMO. The Genki series is one that is often recommended for those not working from a class, since it discusses the material in English.