The horse ran down the hill and through the meadow.

Is this correct?

yes

How come? Shouldn't there be a comma before and?

No. This is a simple sentence: one subject and one verb.

Hmm.. Okay thank you.

Do you understand the differences among the types of sentences? Simple, compound, complex, compound-complex. Basic comma uses are based on understanding these structures.

I will look into that, once I am done with my test. I promise. I have gotten the hang of some stuff.. but I am still working on the others.

Here's a good place to start:

http://grammar.ccc.commnet.edu/grammar/sentences.htm#sentence_types

This is one of the best grammar/usage/writing websites I've found. The Index is the best way to find what you need.
http://grammar.ccc.commnet.edu/grammar/index2.htm

Works great ! Thank you.

Yes, the sentence "The horse ran down the hill and through the meadow" is grammatically correct. It follows the basic subject-verb-object structure, where "horse" is the subject, "ran" is the verb, and "down the hill and through the meadow" is a prepositional phrase that describes the action of the horse.