What is the best way to interview substitute caregivers?

Thank you Lilliput. I'll begin the process this week. Many of your suggestions I hadn't thought about but will use moving forward.

If you go through a reliable agency they will screen for you. Just let them know the things you will need done and if your parent has a preference of gender, age, personality, etc. This is probably your best option if you only need temporary or substitute help because they can get someone to you quickly.
If you are screening privately, it depends on how thorough you want to be. You can have a background check done. Ask for local references. Ask about certificates (CNA, etc.) and what type of caregiving experience they have. You will want to have three recent references along with phone numbers and then, call them. I have a page that lists all the duties that may be expected and ask if there is something they do not feel comfortable or qualified doing. (I especially ask about personal care, bathing etc., and how they do it.)
In the past I used agency care. There are not many agencies where I live now, so I hire privately. The down side for you may be that they will want more hours.
The folks I have hired have been great. I asked for referrals from friends and acquaintances who have lived here awhile. My bottom line is that if I feel uncomfortable with someone during the interview, I move on to the next application.
good luck