Make sure you have read the legal bit on my home page.
As I have already said, the polite desu form of Japanese is the one you are most likely to need and the one other foreigners in Japan will generally use.
The other form which you might need is variously called "plain form" and "dictionary form". It is used in the following circumstances (the list is not exhaustive):
Plain form is not particularly difficult, but there are a few tricks.
Trick one: i-adjectives are their own plain form. Simply leave out the desu.
Polite form: saburinasanhaurusaidesu. "Sabrina is noisy."
Plain form: saburinasanhaurusai. "Sabrina is noisy."
Trick two: in technical writing, the plain form of desu is dearu.
Polite form: mahoutsukaisamahayuumeidesu. "The magician is famous."
Formal report: mahoutsukaisamahayuumeidearu. "The magician is famous."
Tricks apart, the plain form of desu is da.
Polite form: saburinasanhakireidesu. "Sabrina is pretty."
Between friends: saburinasanhakireida. "Sabrina is pretty."
Polite form: saburinasanhaoshyaberidesu. "Sabrina is a talkative person."
Between friends: saburinasanhaoshyaberida. "Sabrina is a talkative person."
That wasn't so bad, was it?
In case you were wondering, the past tense of da is da,ta, the negative is jyanai and the past tense negative is jyanaka,ta.