USE and FORM
POSSESSION
ACTION
have got (= have)
have (without "got") 
have got a pet/ a dog (animals)
have got a book/ a house/ DVDs (things)
have got a brother/ a sister/ a friend (people)
have got straight hair/ green eyes (appearance)
have got a cold/ a headache (illnesses) 
have got an idea
have breakfast/ lunch/ dinner
have a shower/ a bath
have coffee/ a sandwich
have tea/ fruit for breakfast
have a party/ a picnic/ barbecues
have a good time
I / we / you / they
I / we / you / they
+ They have got a pet. + They have breakfast in the mornings.
- They have not got a pet.  - They do not have breakfast in the mornings.
? Have they got a pet? ? Do they have breakfast in the mornings?
he / she / it
he / she / it
+ He has got a pet. + He has breakfast in the mornings.
- He has not got a pet. - He does not have breakfast in the mornings.
? Has he got a pet? ? Does he have breakfast in the mornings?
 
Speaking about possessions
we can use "have" or "have got" both in British and in American English.
I've got a house. = I have a house.
 
But!
  • the form "have got" is more common in British English. - I've got a house.
  • the form "have" is more common in American English. - I have a house.
Speaking about actions
we cannot use the form "have got".
I have breakfast at 7 o'clock. (Not: I have got breakfast at 7 o'clock.)