Japanese language (and society) is quite fixated on social status. This is often reflected by the way you bring yourself (and others) up during a conversation. For the most part, your relationship(s) to other people can be indicated simply by your choice of pronouns. Choosing the wrong pronouns can have unfortunate implications, so it's important to understand their appropriate contexts before engaging in everyday conversation.
Personal Pronouns (i.e. yourself)
watashi - This is the most common (and safest) personal pronoun. This is how you will typically refer to yourself. watashi is technically on the polite side, so its usage is flexible enough for both formal and colloquial settings.
boku - Males will sometimes use this in the company of other males, especially friends or close associates. It's very colloquial, so you would never use it in a formel setting. Girls may sometimes use boku to convey a tomboyish nature. It's also worth noting that boku has become fairly common among gay males, so using it with overwhelming frequency may cause others to ponder your sexual orientation. Um... yeah.
ore - This is an extremely masculine pronoun, and most definitely not suitable for formal situations. You would use this only in the presence of very close male friends and associates, sometimes to assert yourself as leader of the pack. In some cases, it can make you sound cool and laid back; in others, it can make you come off as a punk or a bad boy, especially if you use it in all general situations.
Second Person (i.e. the person you're speaking to)
anata - This is a very polite way of saying you. Although suitable for formal settings, it can at times come off as too endearing. For instance, if anata is used by a wife to address her husband, it more likely translates to dear or darling.
kimi - Typically an affectionate way of saying you, but it's actually pretty informal. You would likely address your close (probably female) friends this way, but definitely not your teachers, superiors, bosses, etc.
omae - Either very laid back or very rude, depending on the situation. You would likely use this among very close friends, but if used to address a perfect stranger, it may seem contemptuous. Like ore, omae conveys a sense of superior status or masculinity.
It's common practice to suffix names and second person pronouns with honorifics, which usually convey a sense of respect for the person you're addressing. Although common, honorifics are not mandatory, nor are they an aspect of Japanese grammar itself. Their usage is entirely elective.
Below are a few examples of some of the more common suffixes:
-san - Similar to to English sir or ma'am. -san can be used safely in most settings, regardless of the nature of your relationship to the listener.
-sama - A more formal version of -san. You may consider using -sama to address teachers or other superiors.
-chan - Implies endearment. This would typically be used to address children, or maybe close female friends.
-kun - Also implies endearment, but in a more masculine sense. Girls may use -kun to address their male friends or little brothers. I suppose males can also use it to address other males.