By "the Realtor," if you mean the listing broker hired by the seller to market the home, you can often click on the "Provided by:" link to the listing broker's company to obtain contact info. If the property is not listed for sale, then of course, there is no Realtor involved. Also, some brokers are fee for service, and only provide their clients an MLS listing. They usually expect you to contact the property owner directly. One way to contact the listing broker, is to drive by the property and obtain the contact information from the yard sign, if you are looking for a specific property.
As a prospective buyer, it is usually best to find someone who could represent your interests as a buyer, since the Realtor that works for you will have access to all the listings in the area of town you are interested in, and can help negotiate for you.
You can also do a thorough search of all properties currently listed in the Birmingham MLS yourself at my website.