General Help on Query Writing, With Defined Schema

Greetings all.

Let's say I've got a database schema like this (with the all-capital terms
in [ ] being the table name) in a PostgresSQL DB:

= = = = = = = = = = = = = = = = = = = = = = =
[PARTY]
PartyID (primary key)
Description
Location

[PARTY_THEME]
Party_ThemeID (primary key)
ThemeID (foreign key 1)
PartyID (foregith key 2)

[PARTY_HOST]
Party_HostID (primary key)
PartyID (foreign key 1)
HostID (foreign key 2)

[THEME]
ThemeID (primary key)
Name

[HOST]
HostID (primary key)
Name
= = = = = = = = = = = = = = = = = = = = = = =

The context here is that I'm a guy with little SQL experience that has to
test this schema for various things before go-live. (Writing what will
essentially be data-integrity test cases as we go forward.) So what I did is
break up the requirement for how the data gets treated and then what I
believe my "test SQL" needs to be:

Requirement: Each party can have one or more themes.
Test SQL: Verify that each PARTY entry has one or more themes after being
entered.

Requirement: 10 parties will be added per week.
Test SQL: Verify that ten parties are in the table at the end of the week.

Requirement: Each party will be assigned one or more host names.
Test SQL: Write a query that checks this after a party is entered.

Requirement: Each party will be assigned one (and only one) location.
Test SQL: Write a query taht checks this after a party is entered.

So what I have is the basic ideas for what I think I should be testing. My
question: is there a resource that can help me figure out how to do this? (I
do know how to write a really basic SELECT statement but what I'm not so hot
at yet is going between tables or knowing how to cross-reference
information, which I think is what I mostly need to do.)

Any help (whether general or specific) is much appreciated.

- Jeff