If you're employed, start with the company you work for. Many companies are starting to provide services to help employees with work/life balance, including providing information and referrals for geriatric
care managers. This is a new trend because studies have come out finding that people on the job who are also primary caregivers are more likely to be stressed and depressed and to have lower work productivity. Check with your Human Resources (HR) department to see if they have resources for eldercare -- and whether those resources are covered as part of your company's benefits plan.
If you don't have any help available from your work, start by finding a geriatric care manager who can do a professional baseline assessment. This assessment can save you time and money in the long run because it helps you find out what level of care your loved one needs. Some people need a trained nurse; others who are at a higher level of functioning may just need a companion or a personal care assistant a couple of days a week. Caregivers have a lot of different kinds of expertise, and if your loved one has Alzheimer's or another form of dementia, you'll want to find a caregiver who has that expertise and experience.
You could also try to find a caregiver on your own, but keep in mind that if you just start searching for a companion, you're going to have to take time off work to do that. There's a real art to choosing and hiring a caregiver; you may have to go through a few different people before you find someone who's a good fit. You're much more likely to get the kind of companion you need with the first try if you get a professional to manage the situation.
If you can't afford to hire a geriatric care manager, find an in-home care agency that will send an employee out to do an assessment before assigning someone to the position.