Quick answer
Одну́ мину́ту.
adnú minútu — in the accusative, because it answers “for how long”
The options
Одну́ мину́ту.One moment.
Мину́точку!Just a second! — softer, very common
Сейча́с.Right away.
Секу́ндочку.One second.
Подожди́те, пожа́луйста.Please wait.
Why мину́ту
A duration answers the question как до́лго? and takes the accusative: одну́ мину́ту, две мину́ты, час. The diminutives мину́точку and секу́ндочку are what people actually say — they sound friendly rather than curt.
Сейча́с
Сейча́с literally means “now”, but as a one-word answer it means “I am on it”. Said slowly, сейча́-а-ас, it means the opposite.
What you hear back
Коне́чно.Of course.
Не спеши́те.Take your time.
Хорошо́, я подожду́.Fine, I’ll wait.
Typical mistakes
Одна́ мину́та.
Одну́ мину́ту.
Duration goes in the accusative.
Подожди́ — to a stranger
Подожди́те
Use the polite plural with people you do not know.
Check yourself
Which form is correct?
Accusative for a length of time.