A simple sentence consists of one independent clause, meaning it contains a subject and a verb, and makes one complete thought. Examples of simple sentences are below, with subjects and verbs in boldface:

I am learning. We both dislike pungent cheeses. With eagerness, the fox ran over past the hill to the farmer's chicken coop. She and I have fun. (compound subject) He took and passed the test. (compound verb)

For more help with simple sentences, check out the following entries in Write it Right With Strunk & White:

Rule 6: