3 Answers

I know how to parse a sentence, but diagram? I have not heard that expression before. Is this New-speak?

Girls' fast-pitch softball team and boys' baseball teams used the muddy field and went home messy.

Girls" fast-pitch softball     are adjectives modifying the noun/subject:  team 
boys' baseball are adjectives modifying the nounsubject:  team
 
used is the first verb/predicate   
the muddy are adjective that modify the noun field 
The phrase "the muddy field" describes what was used, and I don't know what that would be called in relationship to the verb.  
and is a conjunction which joins "used"  and "went" as the compound predicates. 
went  is the second verb/predicate
home is a noun, but also describes where the teams went, and I don't know what that would be called in relationship to the verb.
messy is describing how the teams went home, which would make it an adjective.  

Sorry I can't give you better information.   

After using the muddy field, the girls' softball team, and the boys' baseball team went home messy.

I always thought that softball and baseball were the same game.