You've already learned the phrases すみません and 失礼します for apologizing. A third way to apologize yourself is to use the phrase ごめん なさい.
| I'm truly sorry. | 本当 に ごめん なさい。hontou ni gomen nasai. |
ごめん なさい can be used after a verb in the て-form to excuse yourself for an action.
| Please excuse my being late. | 遅れて ごめん なさい。okurete gomen nasai. Sentence from Tatoeba |
| Please forgive me for forgetting to call you. | 電話するの を 忘れて ごめん なさい。denwasuruno o wasurete gomen nasai. Sentence from Tatoeba |
Note how in the last sentence の is placed after the first verb to turn it into a noun.
When asking permission to enter someone's house you can say ごめん ください. When you are allowed inside, it is polite to say お邪魔します.
| May I come in; Please forgive me. | ごめん ください。gomen kudasai. |
| Please come in. | どうぞ 入って ください。douzo haitte kudasai. |
| Excuse me for interrupting you; Used as a greeting when entering someone's home | お邪魔します。ojamashimasu. |
