Japanese honourifics (敬語, keigo) are divided into 尊敬語
sonkeigo, respectful words, and 謙譲語 kenjyoogo, humble words (excuse the
romanisation). The use of each depends on the notions of "out-group" and "in-group".
Honourific verb forms are where a bit of irregularity creeps into the language. There are both regular forms, which may be arrived at by conjugation, and irregular forms. The regular way to construct a respectful verb, is to prefix the verb stem with "o", the honourific prefix, and append "ni narimasu".
Example:
kaku->kaki->o-kaki ni narimasu
書く → 書き → お書きになります
Of course, the narimasu ending is conjugated to arrive at all the other possible verb manipulations.
In addition to regular respectful verb formations, there is humble verb formation. This is done by prefixing the verb stem by "o" and appending "shimasu" or perhaps "itashimasu" (more on this later) to the verb, similar to forming respectful verbs.
Many common verbs also have irregular respectful forms and humble forms, e.g. suru, which has the humble form of "itasu", and the respectful form "nasaru". Other common examples are:
-Iku (to go) : Respectful form of irassharu, humble form of mairu
-Iru (to exist) : Respectful form of irassharu, humble form of oru
-Iu (to say) : Respectful form of ossharu, humble form of mousu
-taberu (to eat) : Respectful form of meshiagaru, humble form of itadaku
-shiru (to know) : Respectful form of gozonjiru, humble form of zonjiru
Of course, there are others.
The meanings of the irregular respectful/humble forms often interrelate closely to their use in keigo, and are also the source of many "set phrases" that Japanese students are taught (like itte mairimasu, itadakimasu, etc). Mairu, for example, is defined as going up/going into a higher/sacred place.
In addition to this are the nouns, which are easier. Respectful nouns may be simply formed by adding the prefix "o" or "go" onto the noun. Which prefix is added is irregular! A general rule is that if the noun is read using kunyomi, e.g. namae (name), the prefix is often "o", giving "onamae". If the noun is read using onyomi, e.g. juusho (address), it is often "go", giving "gojuusho".
Also, there are many nouns, most of which are Chinese words that are intrinsically respectful in tone. If you use "otaku", for another person's house, it is more "formal" in tone.