Polite Japanese 敬語

There are three basic types of honorifics for verbs. It depends on your social rank as to which form to use.

A) Humble (謙譲語 kenjougo) - This is when referring to oneself or one's family members and (usually) speaking to someone higher up in social rank, position or some other criteria for determining status. However even some people with high positions may choose to use the humble form with those under him/her.
B) ~masu - As mentioned above ~masu / desu is actually 丁寧語 teineigo or polite language, but I'm using the familiar ~masu form for an easy comparison to the the kenjougo and sonkeigo forms.
C) Respectful (尊敬語 sonkeigo) - This is what you say to your boss or those higher up when speaking to them. If you are speaking about yourself, you will use the humble form.

Humble
(speaking to your boss about yourself)
Normal
(speaking to your friends)
Respectful
(speaking to your boss about your boss)
拝見します
haiken shimasu
見ます
mimasu
to see
ご覧になります
goran ni narimasu 
申します
moushimasu
You know this from "name to moushimasu"
言います
iimasu
to say
おっしゃいます
osshaimasu
頂きます
itadakimasu
食べます
tabemasu
to eat
召し上がります
meshi agarimasu

参ります
mairimasu

This is the humble form for both to come and go!

来ます
kimasu
to come

行き