How do I write a compound sentence?

A compound sentence is when two independent clauses are joined together and connected with a comma and a conjunction.
An independent clause is one that expresses a complete thought. It is called independent because it should be able to stand alone as a complete thought. It must have a noun and a predicate (subject). For example: Paul ran down the street.
The clauses are connected with a conjunction. A way to remember the options for conjunctions is the mnemonic device FANBOYS. Fanboys stands for: for, and, nor, but, or, yet, so. The job of the conjunction is to connect the two independent clauses. The comma comes before the conjunction
Example:
independent clauses:
Paul ran down the street.
He fell off his bike.
Compound sentence:
Paul ran down the street, and he fell off his bike.
As you can see, the two parts of the sentence are independent and can stand alone, but they are connected with a comma and a conjunction.

A simple sentence is an independent structure that has a subject and a verb , and it expresses a complete idea. When you have 2 independent clauses ,you can put them together and create a compound sentence. To do so, you will need to use linking words, also known as coordinating conjunctions. These are: for, and, nor, but, or, yet and so. (You can use the word FANBOYS as a way to remember their initials and bring them to your mind quickly)
Each of these words will indicate the relationship between the 2 ideas you are linking.
for: reason
and: addition
nor: disjunction
but: contrast
or: alternative
yet:concession
so: result
Do not forget there must be a subject and a verb in each part of the sentence ( each clause) for it to be a compound sentence! Also take into account we write a comma before the linking word.
examples: Mary did the cooking, and her husband did the washing.
The show is interesting, but the tickets are too expensive.
You can pick up the parcel at the office, or they can send it to you .

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.