I am having a hard time trying to figure out when to use a 1-to-1 relationship in db design or if it is ever necessary.
If you can select only the columns you need i
Often people are talking about a 1:0..1 relationship and call it a 1:1. In reality, a typical RDBMS cannot support a literal 1:1 relationship in any case.
As such, I think it's only fair to address sub-classing here, even though it technically necessitates a 1:0..1 relationship, and not the literal concept of a 1:1.
A 1:0..1 is quite useful when you have fields that would be exactly the same among several entities/tables. For example, contact information fields such as address, phone number, email, etc. that might be common for both employees and clients could be broken out into an entity made purely for contact information.
A contact table would hold common information, like address and phone number(s).
So an employee table holds employee specific information such as employee number, hire date and so on. It would also have a foreign key reference to the contact table for the employee's contact info.
A client table would hold client information, such as an email address, their employer name, and perhaps some demographic data such as gender and/or marital status. The client would also have a foreign key reference to the contact table for their contact info.
In doing this, every employee would have a contact, but not every contact would have an employee. The same concept would apply to clients.