Sentence

A simple sentence consists of only one clause.
A compound sentence consists of two or more independent clauses.
A complex sentence has at least one independent clause plus at least one dependent clause.
A set of words with no independent clause may be an incomplete sentence, also called a sentence fragment.
A sentence consisting of at least one dependent clause and at least two independent clauses may be called a complex-compound sentence or compound-complex sentence.

1. I like trains.
2. I don't know how to bake, so I buy my bread already made.
3. I enjoyed the apple pie that you bought for me.
4. The dog lived in the garden, but the cat, who was smarter, lived inside the house.
5. What an idiot.

Sentence 1 is an example of a simple sentence.
Sentence 2 is compound because "so" is considereda coordinating conjunction in English, and sentence 3 is complex.
Sentence 4 is compound-complex (also known as complex-compound). Example 5 is a sentence fragment.

The simple sentence in example 1 contains one clause.
Example 2 has two clauses (I don't know how to bake and I buy my bread already made), combined into a single sentence with the coordinating conjunction so.
In example 3, I enjoyed the apple pie is an independent clause, and that you bought for me is a dependent clause; the sentence is thus complex.
In sentence 4, The dog lived in the garden and the cat lived inside the house are both independent clauses; who was smarter is a dependent clause.
Example 5 features a noun phrase but no verb. It is not a grammatically complete clause.