When someone else does a job for you (you arrange it, you don't do it yourself), use have + the thing + the past participle. The thing goes in the middle.
have + the thing + the past participle
I don't wash the car myself. / I have the car washed. (someone does it for me)
Someone services the car. → We have the car serviced.
A dentist checks his teeth. → He has his teeth checked.
Not "I washed the car myself. (you did it)" — say "I had the car washed. (someone did it for you)". Put the thing in the middle: have the car washed, so someone does it for you.
Try it: She arranges for a mechanic to check her brakes. A mechanic checks the brakes for her. Build what she says she does. Answer: She has her brakes checked. — Someone does it for her, so the thing goes in the middle and the verb is the past participle: She has her brakes checked. "Checks" would mean she does it herself, so leave it out, this is have + the thing + the past participle.
get + the thing + the past participle
get works the same way and is a little more relaxed: get + the thing + the past participle. Same meaning as have, just more everyday.
A mechanic repaired my car. → I got my car repaired.
A salon did her nails. → She got her nails done.
Painters are doing the kitchen. → We're getting the kitchen painted.
Try it: A tailor fixed his suit. A tailor fixed his suit for him. Build what he says. Answer: I got my suit fixed. — Someone did it for you, so put the thing in the middle and use the past participle: I got my suit fixed. "Fix" is the base verb and would break the pattern, so leave it out, it's get + the thing + the past participle.
Word order: the thing sits in the middle
The thing always goes between have/get and the past participle. If you move it to the end, the meaning changes.
have the car washed = someone washes it for you ✔
have washed the car = you did it yourself (a different tense) ✘
get your hair cut = someone cuts it for you ✔
Not "I have washed the car. (you did it)" — say "I have the car washed. (someone does it for you)". Keep the thing in the middle — have the car washed — or it sounds like you did the job yourself.
Try it: A photographer is taking their photo. A photographer is taking their photo for them. Build what they say. (Leave out the word you don't need.) Answer: We are having our photo taken. — Someone is doing it for you, so the thing goes in the middle and the verb is the past participle: We are having our photo taken. "Taking" would mean you take it yourselves, so leave it out, the thing always sits between have/get and the past participle.
Saying no and asking questions
To say no or to ask, use do / does / did — just like any other verb. Now have/get goes back to its base form, but the thing still sits in the middle and you still use the past participle.
No: I didn't have the car washed. (nobody washed it for me)
Ask: Did you get your teeth checked?
Ask where/when: Where did you get your hair cut?
Not "Did you had your teeth checked?" — say "Did you have your teeth checked?". did carries the past, so have drops back to its base form — but the thing stays in the middle and the verb stays the past participle.
Try it: No one fixed her phone for her. No one fixed her phone for her. Build the negative. (Leave out the word you don't need.) Answer: She didn't get her phone fixed. — "didn't" already carries the past, so "get" stays in its base form, not "got". The thing (her phone) still sits in the middle and the verb is the past participle: She didn't get her phone fixed.
Try it: A salon cut her hair — you want to check. You want to ask a friend if a salon cut her hair for her. Build the question. (Leave out the word you don't need.) Answer: Did you have your hair cut? — "Did" starts the question and carries the past, so "have" stays in its base form, not "had". The thing (your hair) still sits in the middle and the verb is the past participle: Did you have your hair cut?