Well your options are book a normal cruise and try a guarentee share program, Princess and Holland america have this. I belive you must book directly with the cruise line though, so the prices might be high. You get the price you agree on and they find you a same sex cabin mate if not you get the cabin to yourself with no singles supplement. But you won't find many singles on a normal cruise. There is usually a singles party on every cruise but the number may be slim to none. So be prepared just to enjoy a nice vacation, and try to mingle and talk to people to make friends.
You can post a message on this site under "seeking cruise companion" forum and try to meet another single travel partner. Or book with friends. Last minute travel is cheaper if you can do it. So is traveling with a group such as a cruisemates group cruise. There is also a travel chum web site to meet potential travel partners.
Or save your money longer and book the escorted singles cruise. Check all the agencys look for the (Singles cruise calender) on this site, and search all the companies, the 3 and 5 day singles cruises are cheaper. So is an inside cabin.
Over all they are more expensive then a normal cruise but they are more fun since you have a group to hang out with.
No guarentees on finding anyone your attracted to, though so go with the intent to make friends and for the travel experiance first, not to meet a guy or you could be disapointed. Romance is a possibility, so is a meaningless fling just keep your eyes and ears open, some guys are looking for just one thing. It's up to you. I think the experiance of hanging out with a group of singles makes paying a bit more worth it at least your not stuck with all couples and familys.