A good place to start is right here on the internet, since you are already here. 
 

While you are at the web sites of other teachers, check out their lists of students, or ask them if they know of a reputable teacher or Reiki healer in your area.  It's also possible that the teacher may even travel to your area if you can get a group together large enough to cover her or his expenses.   Some teachers might even give you the class for free if you can do this.  You can always negotiate this.

If the internet doesn't give you any good results, then the next place to look might be a local bookstore; not necessarily one of the large chains, but a smaller store that might allow flyers, pamphlets and/or business cards to be displayed. You can also ask the store personnel if they know Reiki teachers or where you could find someone who teaches Reiki.  At least they are likely to have heard of Reiki.

The bookstore may also carry locally published free newspapers or magazines that may have advertising or classified pages for holistic teachers and practitioners.  If you don't see Reiki listed, don't be afraid to call some of the people listed to see if they know of any teachers, or where to look.
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Another source may be some of the smaller restaurants in your area - especially those that allow bulletin boards and flyers.  Check the health and nutrition-conscious eating places.  Their employees may also have an idea who teaches Reiki in the area - often it might be one of their own customers.

From there you can try health food stores or nutrition suppliers (places that sell vitamins, etc.), herbal stores (selling herbs, essential oils, etc.) or any shop or service that promotes alternative healing.

One place that is often overlooked is the neighbourhood laundromat.  Often there is a bulletin board and you might find a posting from a teacher very close to you.  Another good place to look is a community centre.  Again you can ask the people who work there.

Coming back to the internet, if you are still having difficulties then another idea is to ask other Reiki practitioners on some of the Reiki lists at Yahoo, MSN and elsewhere.  For example, you can log onto Yahoo Groups at http://groups.yahoo.com/ and search for Reiki groups.  One very reputable one is the URRI list. 

Another Internet source are the various Reiki directories.  There are a few listed at my Resource Page and my Reiki Reciprocal Links Page

I hope you are successful in locating the right teacher (or practitioner) for you.