For the first four months I used a website called
Nihongo Master to learn the basics such as reading and writing the hiragana and katakana as well as some basic grammar. Then I found a private company in my area that teaches Japanese and I've been going there for a year now. They use the Genki I and II textbooks, which are pretty good.
If you're motivated enough and have the right materials, then self-study is possible. But if there is an option available to study in a classroom setting, I highly recommend it.