I worked as a nanny for several years, most of them spent in a small town. Unfortunately in small towns it's usually about who you know and word of mouth. So, moving to a new town that's going to be a disadvantage to you. One of the first things I would do would be to get involved in the community, in the local church (if you're at all religious), in general be involved in the fabric of the town life so that when you apply for nanny/babysitting jobs, people will have an idea of who you are...and if they don't know, chances are their neighbor, friend or someone does and can fill them in. Also, since you're going to be new to the area and few if any people will know you, you'll want to be certain that your references are impeccable and up to date. Have at least four or five written references from people for whom you have either been a nanny or a babysitter, along with their contact information (phone number, etc.) should the prospective parents wish to follow up with further questions. Also have personal references avaialable for the prospective parents. These can be from your minister, previous (non-nanny) employers, long-time friends (particularly if they have some standing in their community; think: lawyers, doctors, teachers, etc.), also have contact information available for parents to follow up on these references as well. Also, be prepared to submit to a background search if the parents request it.
Once you've made sure all your ducks are in a row, start looking in the local paper and answering ads for child care help, casually let people know that you are interested in working as a nanny/babysitter/mother's help, etc. Keep in mind that nannies in smaller towns generally live-out and typically do not receive as high a salary as ones in bigger cities.
Good luck with your search.