V3 here represents the Past Participle, a form you find in the third column of a table with irregular verbs.
WIth regular verbs, just add -ed to form it:
In informal settings, you can use GET instead of HAVE. The meaning will remain the same.
I need to have my hair cut.
I need to
get my hair cut.
HOW DO I USE IT IN DIFFERENT TENSES?
Just put have/get in the required form. You don't have to do anything about the Past Participle (V3) of the main verb.
She has/gets her hair dyed once a month. (Present Simple)
is having/getting her hair dyed today. (Present Continuous)
had/got her hair dyed two weeks ago. (Past Simple)
has just had/got her hair dyed. (Present Perfect)
is going to have/get her hair dyed. (be going to)
had had/got her boobs done before she had/got her hair dyed. (Past Perfect)