Simple:
* The sun was shining, and the birds were singing.
* The dog barked, but the cat ignored him.
* I went to the store, for I needed milk.
* She finished her homework, so she could go to the park.
* He loves to read, or he likes to watch movies.
More Complex:
* The storm raged outside, yet the family was safe inside their home.
* The train was delayed, and I missed my appointment.
* She wanted to go to the concert, but her parents wouldn't let her.
* He was tired, so he decided to take a nap.
* I will go to the beach, or I will stay home and read.
Using different conjunctions:
* The cat is sleeping, while the dog is playing. (while)
* I like pizza, nor do I like pasta. (nor)
* She is a talented singer, yet she is shy. (yet)
Remember: A compound sentence has two or more independent clauses joined by a coordinating conjunction. An independent clause is a group of words that can stand alone as a complete sentence.