The opening paragraph should always contain the reason for writing. So something like this might be appropriate -
Dear Sir/Madam
(try to find out their name if possible and use it)
I am writing to enquire whether you have any vacancies for ... at the moment.
The next paragraph should say something about yourself. I am X years old and have previously held a similar position/ recently finished my studies. ... The third paragraph should ask for the application form. Should you have any vacancies I would be most grateful if you would send me the appropriate application form. My address is ... If you have no vacancies at the moment, I would much appreciate it if you keep my name on file and consider me for any vacancies that may arise in the future. Finally.
Thank you for your assistance in this matter. I look forward to your reply.
Yours faithfully (Yours sincerely if you use the persons name above)
...
Hope that helps
Good luck with the job hunting!