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: