Which is right to say and why?

There were a dog and a frog on a log.

When you start a sentence with there is or there was, the subject is actually the noun that follows.  In this case, you have a compound noun (a dog and a frog), which is plural.  So were is the correct choice, as Sanjay pointed out.  However, this sounds awkward since a dog is closest to the verb, making it sound singular to our ear.  If you switch the sentence around so the subject is first, as in most sentences, it will sound better.  A dog and a frog were on a log.