For the record, I don't believe in ghosts, but I don't DIS-believe either... if someone came up with hard proof tomorrow I'd be totally willing to hear them out, just because we don't have the evidence of, or science to prove the existence of something, doesn't mean it's not real. It wasn't that long ago (relatively speaking) that you would have got stoned for saying the earth was round or excommunicated for saying it wasn't the center of the universe. If you really believe in science you can only believe in things that we can prove, you can't say an unproven hypothesis is definitely wrong, we discover new and crazy stuff every day.
That being said, lets assume for a second ghosts exist and are in some way susceptible to the laws of physics (if they can be seen, they can be photographed, they're not just projected straight into our minds)
- first off, I would have it VERY explicit in your contract that payment in no way depends on actually producing a photo of a ghost. You are being contracted for X number of hours or Y number of shoots and you're being paid for the ATTEMPT to photograph a ghost.
- with that clause though comes some trust, you will have to be perceived as actually trying to photo a ghost for the entire time you're contracted. No slacking off and saying "ooops, guess no ghost" at the end. So make a list of all the things you are going to attempt and get a list from your employer (whom I'm hoping has some paranormal background you can draw from) of what s/he wants you to do.
- along with still photos, I would employ video. There are subjects we KNOW exist that are hard to capture with stills, which require video to ever hope to catch a few frames. If you don't have the equipment, take a look at getting a few GoPro's and pass the bill to the employer if possible.
- how to actually photograph them, the only suggestion I have is to use nothing but natural light, as any kind of artificial light source could be used to disprove your photo by causing weird light artifacts, reflections, halos, flares etc.
Now lets take the other situation, ghost exist but are projected directly into our minds, they have no physical presence that can be photographed. In this case the only way to "photograph" them would be to hook up a monitor of some kind to the brainwaves of the subject and record their reaction during a sighting. You would need a baseline to compare with. Lets assume the subject feels fear when they see a ghost, you'd need a recording of their brainwaves during times of different levels of fear, then normal fear activity (adrenaline, flight/fight responses etc) can be eliminated from the "ghost" reading and see if any areas of the brain are being activated that aren't during normal fear responses.