Would you please help me with problem? Thank you.
If I take a day off from my work am I supposed say:
I have a vacation day.
I have a holiday.
Which one is appropiate?
This is a British/American English difference. In Britain you would take a day's holiday in the US, you'd take a vacation.
The word "holiday" tends to be a national event such as Thanksgiving in the US, while "vacation" isn't in common use at all in Britain.
In the work situation, and taking some or all of one's annual leave, a person would say, "I'll be on holiday till..." if paid a wage, but a person on a salary would say, "I'll be on leave till..."
A person on a salary taking a day off would refer to it as "taking a leave day". I am unsure how a person on a wage would phrase it; but be aware, whether salary or wage, a person taking the day off and reporting in ill when they are not - they just want a day off - would refer to it privately (NOT to their employer) - as 'taking a sickie'.
If you are asking in connection with your own work situation, why not say/write, that you wish to take a day of your annual holidays to attend a funeral/wedding/child is sick - whatever the legitimate reason is.