Bacially, we use 常体/くだけた言い方/普通形/informal/plain for between close people, I mean, between family members, close friends, etc. (Note: all depends on the family, age, friendship between you and your friends. There's no specific rules but we have to take care of the use of informal form.) We use 敬体/敬語/丁寧形/丁寧語/formal/polite form in the bussines situation, to the people who are older than me and in higher status than me, and whom I don't know well, for example when I ask the way on the street. (Note: I use the formal form to my friends who are older than me, it depends on the person.) I hope this helps you.

Probably you means 敬体 as 敬語 and 丁寧語, which are polite form, and 常体 as plain form. We usually use polite form when we talk to new people except obviously younger persons than the speaker. When you and the people become friendly, you should use plain form.