I use basic Japanese grammar knowledge, which along with the 2 basic letter types (hiragana, katakana) can probably all be learned in 1-2 weeks if you give care to try.
And rikaikun, an extension that attempt to translate a single word that my mouse icon hovers on.
Basically so long as I can tell 'X do B to Y', I can translate each of the words individually and get a basic grasp of things, then over time build up visual recognition of things.
(Of course it's not fool proof since it requires you to actually consider the multiple meanings a word can have, one of the most often mistranslated is a term that can be both rape and insult....let's just say people use the latter way too often despite the former being the one the story obviously meant)