How do I go about hiring an individual to provide in home care for my mom?

Start by checking the employment laws for your state. The IRS gets to decide who is an employee. If someone works for you for a consistent amount of hours and you are their only client, in most cases this can make you an employer (there are more criteria than this). You cannot pay them in cash. You must comply with the withholding rules and tax laws. Make sure you do a background check and always have a written contract.

While you contact an agency keep in mind they are working for you. You contact an agency and say you would like a caregiver between the hours of XX:XX Am and XX:XX Pm.
It is more difficult if you and help in the morning and then again in the late afternoon. A split shift is harder to fill.
If you hire privately please make sure you have a caregiver contract in place. Make sure that background check is done. I would also make the contract reviewable in 6 month spans. As a person declines more help is necessary and the person you hire needs to be able to handle the decline and with decline a pay increase might be warranted.

randyanders123, what time frames are you looking for? Most caregivers would like either part-time such as 20 hours a week, or full-time at 40 hours a week. And with set hours, especially for those who work part-time as they maybe working part-time set hours for another client.

If you are looking for on-call caregivers, that could be tough. I hope you do find someone.

Oh, if you hire someone directly, they become your "employee". You would need to contact your home insurance carrier regarding "workman's comp" insurance in case your employee gets hurt on the job.

Ask people you know if they have any referrals they can suggest