Did is used in the Simple Past Tense.
E.g. (1) I went to school. (Simple Past)
= I did go to school.
(2) Raju came late. (Simple Past)
= Raju did come late.
(3) We played football. (Simpe Past)
= We did play football.
Does and Do is used for Simple Present Tense.
(Does for single person, Do for more than one person except subject `I')
(1) I go to school. (Simple Present)
= I do go to school.
(2) Raju come late. (Simple Present)
= Raju does come late.
(3) I come late. (Simple Present)
= I do come late.
(4) We play football. (Simple Present)
= We do play football.