With the approaching Yomim Norayim thoughts of doing a proper teshuva (repentance) is at the front of many people's minds. Many times we sin and regret our choices; we truly want to do teshuva, but are not aware of how to properly accomplish this.
It is important to mention, teshuva is a mitzvas asei me'doraisa (Biblical commandment). The Torah [Bamidbar 5:7] says "V'hisvadoo es chatosum asher asu" (and they shall confess their sin which they committed). Just as with other mitzvos, the only way to keep it properly is to know the halachos of the mitzvah [e.g. it is impossible to properly keep the mitzvah of Shabbos without the knowledge of Hilchos Shabbos (See Introduction to Mishneh Berurah vol. 3)], the same is true regarding the mitzvah of teshuva.
The Rambam [Hilchos Teshuva 2:7] writes that even though there is a mitzvah to do teshuva each day of the year, on Yom Kippur one is required to do teshuva. Therefore, if one did not do teshuva on Yom Kippur, he has violated a mitzvas asei (see also Sefer Hachinuch 364).
The Mishnah [Yoma 85b] teaches that Yom Kippur atones for sins between man and Hashem, however not sins against one's fellow man. Therefore, one who wronged someone is obligated to appease him (Shulchan Aruch 606:1).
It is important to note, if someone wronged another person, in addition to violating a mitzvah of bein adam l'chaveiro (interpersonal relationships), one has also violated a mitzvas bein adam l'makom (between man and G-d). Therefore, even if one appeased the other person, one is still obligated to repent on the bein adam l'makom aspect of the aveira (Rambam Hilchos Teshuva 1:1, Shaarei Teshuva 1:45 & Shulchan Aruch 606:2).
One is only obligated to appease his fellow man if one caused damage to him (Sefer Chafetz Chaim Lashon Hara 4:12 quoting Shaarei Teshuva 207). For instance, if one said something insulting about someone, however, it was not in front of him [and therefore he was not insulted], nor did it lead to any damage, etc. he would not need to ask forgiveness.
If one did cause harm to someone, even if that person did not know about it, one is obligated to ask for forgiveness (Sefer Chafetz Chaim 4:12). Therefore, if someone said rechilus (literally means bearing tales from one to another)
about someone, if he sees the listener believes him, one is required to ask forgiveness from who he spoke about, because this most probably resulted in some form of damage etc. (Sefer Chafetz Chaim 2:4: BM"C 4).
If one wronged a katan (minor) the custom is to ask forgiveness. Additionally, when the katan reaches adulthood (13 year old boy or 12 year old girl), one is obligated to ask him again, since a minor's forgiveness, is not a halachically binding (Koveitz Halachos [Piskei Harav Shmuel Kamenetsky, shlit"a] 25:17).