An informal application enquiry should read something like the one below. Obviously you need to change any of the details which do not apply to you. If you are not able to fund yourself, do not apply for projects where you do not fit the 'Funding Status' criteria. If English is not your first language try to get somebody to check your letter before you send it.
Dear Dr *supervisor name*
I have seen your research project "*Research Project Title*" on FindAPhD and would be interested in applying. Please send me an application form and any further details you have available.
My nationality is *nationality* and although I am hoping to find a scholarship, I will be willing to fund my own study if necessary. I have just completed an MSc in *subject name* at *university name* in *country name*. My CV is attached for your information.
Best regards
*your name*