How do I add two count(*) results together on two different tables?

Wrap them up and use subqueries:

SELECT
(SELECT COUNT(*) FROM Toys WHERE little_kid_id = 900)+
(SELECT COUNT(*) from Games WHERE little_kid1 = 900 
                              OR little_kid2 = 900 
                              OR little_kid3 = 900)
AS SumCount

Voila!

SELECT
((SELECT COUNT(*) FROM Toys WHERE little_kid_id = 900)+
(SELECT COUNT(*) from Games WHERE little_kid1 = 900 
                              OR little_kid2 = 900 
                              OR little_kid3 = 900))
AS Sum FROM DUAL;

Selecting from the DUAL Table