I'm going to assume that you're already familiar with the concepts of hiragana, katakana and kanji. If not, please check out the wiki entries for them.
I also highly recommend downloading NJ Star. This is a shareware word processor that supports both Japanese and Chinese text. The best part is that NJ Star has an auto-dictionary that can pop up the English translation of words when you put your cursor over them. Eventually, buy it. NJ Star disables the auto-dictionary if you use the free version for more than 30 days. $99 may be a little steep, but it's still a great tool if you're serious about your studies.
You really don't need any other dictionaries if you have NJ Star and if the text is already in electronic format (such as grabbing text from an online PDF). Otherwise, consider getting something like the Casio handheld electronic dictionary, which lets you write in kanji using the stylus and touch pad. This will give you the reading of the kanji, which you can then type into NJ Star. It's also a great way to practice writing kanji at the same time.
Now, if you already have NJ Star and/or a Casio dictionary, looking up individual words will be easy. So, I can skip that part. What is worth explaining are a few major topics that can trip up a beginner.
To be continued...