My dog went to the park. I threw his ball.
Do not join only with a comma--the dreaded comma splice:
My dog went to the park, I threw his ball.
Add all the adjectives and prepositional phrases you want--no commas (generally):
My big lovable dog went to the park in a red wagon with white stripes.
Double the subjects or the verbs, making no changes:
Fred and I threw his ball.
I threw his ball and a stick.
My dog went to the park and rolled in some smelly stuff.
Connect with semi-colon or with comma plus coordinating conjunction ("and," "or," "but," "for," etc.):
My dog went to the part; I threw his ball.
My dog went to the part, and I threw his ball.
Subordinate the first clause and use the comma:
When my dog went to the park, I threw his ball.
After my dog went to the park, I threw his ball.
Because my dog went to the park, I threw his ball.
Subordinate the second clause and (generally) do not use the comma:
My dog went to the park because I threw his ball.
My dog went to the park after I threw his ball.
My dog went to the park, while
I threw his ball.
.