The once tedious and time-consuming task of discovering asteroids has been made extraordinarily simple thanks to modern technology. You may want to start your hunt by setting your field of view near to the location of a known asteroid or an object on the MPCs unusual or critical object list, as there is a good chance that another object will be the field. This is definitely not a must, but is worth a try now and then. Hunting near the ecliptic will also increase your chances of spotting an asteroid, as objects appear less and less bright the farther away they are from the ecliptic.
If you do not have a telescope with motorized slewing, then a good method for hunting asteroids is to focus on a specific field over the course of an hour. During the hour take several exposures of that specific field and repeat the process in another field for an hour as many times as your time and desire permits you. Using the fantastic software of today, you can analyze your results quite quickly. By blinking the images you have for any given field you may discover an object that is clearly moving, and possibly the subject of your hunt!
If you do have a telescope with motorized slewing (or accurate digital setting circles) then your task will be made even easier. You can capture a sequence of images in adjecent fields and increase your chances of success even more- obviously the more fields you are able to get a seqeuence of images on, the better. And as statistics suggest, within a few days of hunting you should score a prize and find yourself contacting the MPC. Of course, you will need to confirm your sighting on at least one other night before they will accept your submission, and you will also need to have to coordinates for your discovery prepared.