Compound sentences simply involve putting together (or "compounding") two sentences with a comma and a joining word (or "coordinating conjunction"). Coordinating conjunctions include and, but, or, for, nor, yet, and so. One of the key parts of understanding compound sentences is knowing that the pieces must be able to stand on their own as independent clauses.
Be careful: Just because you see a comma and a coordinating conjunction doesn't mean the sentence is a compound sentence. For example, "Simon is playing Pokemon, and having a lot of fun" is not a compound sentence. Why not? Because "having a lot of fun" is not an independent clause, and the comma technically shouldn't be there (though very casual writers sometimes add one). The correct version of this as a compound sentence would be:
Simon is playing Pokemon, and he is having a lot of fun.
Let's consider some other examples of compound sentences:
Alice wants to get ice cream at Dairy Queen, but she is lactose intolerant.
Gordon is busy with work, so I went to dinner with Victoria instead.
We will go see Batman v. Superman tonight, or we will stay at home and watch Netflix.