The same way you would look for any job.
You assemble your portfolio along with you CV and a covering letter and you send it to them either via email or via snailmail on a CD/DVD. If you do it that way, please ensure you use a good virus scanner before you create the CD as the best possible way to shaft yourself is to send somebody an infected disk. I know, who would do such a thing! As a recruiter I've received so many over the years it's just second nature as soon as I've received a CD it's scanned by the latest updated Virus Scanner before it's opened. If it catches anything the CD is broken in half and thrown away unread. Could have been a good person but failure to look out for the little things tells me something about that person as well. Not something I'd like to send to my clients.
Anyway, Email or snailmail. If you are IT savvy, you could do a flash presentation or create a small MPG/AVI video where you can speak to them as well so they will also not only see you but hear your voice as well.
I didn't go that route however, as I was introduced by another part-time actor (also Caucasian) and I actually part-time directly for the studio. Most part-time actors work through an agency.
If you are looking at this professionally, this is another avenue you could pursue:
http://www.esma.sg/talent/course/listin ... 09-0000004
Good Luck
SMS