I was wondering if anyone could explain some of the differences between formal, semi-formal and informal Japanese. Thanks!
There are three main levels of politeness in Japanese: teineigo ("standard" polite language), kudaketa nihongo (casual speech) and keigo (very polite/honorific language).
kudaketa nihongo (くだけたにほんご) - used when talking to friends and family, people you are familiar with; it uses da (だ) copula form instead of desu, and verbs take the dictionary form (endind with -ru, -mu, -gu etc).
teineigo (ていねいご) - used when talking to strangers and people you don't know well, who are not close to you; it uses desu (です) copula form and verbs with -masu (-ます) endings.
keigo (けいご) - very polite, honorific forms; further divided into:
sonkeigo (そんけいご) - respectful language, when talking to and about someone of higher status and their family (among other people close to them).
kenjougo (けんじょうご) - humble language, when talking about oneself and one's family (also when referring to one's own boss at business meeting between two companies).
- Example: to eat:
taberu (たべる) - casual (dictionary) form
tabemasu (たべます) - standard polite form
meshiagaru (めしあがる) - very polite form
In formal (polite and very polite) speech, honorific suffixes such as -san (さん) or -sama (さま) are usually used, along with beautyfying prefixes o- (お-) and go- (ご-).
Apart from familiarity, age, social status and rank also play important role when choosing which form to use: you may use casual forms when speaking to someone younger or subordinate, but you should use polite language when talking to elders and those of higher rank, for example your boss.
The higher that person's status is from yours, the more polite you should be.
The topic of levels of formality in Japanese is very vast. I found those articles to be helpful and interesting:
Here's a bit more about the honorific prefixes, suffixes and special humble and respectful forms: (http://www.thejapanesepage.com/grammar/more_polite_language/)
And here are more examples for some common verbs: (http://maggiesensei.com/2009/08/27/%e3%81%91%ef%bc%9a%e6%95%ac%e8%aa%9e%e3%80%80ke-keigo/)
Duolingo's Japanese course from English mostly uses standard polite forms, but some honorific forms appear in phrases and greetings (such as itadakimasu). You may try to spot them all ;) がんばって！^.^