Choose the exact spelling and extension you want to evaluate, then query a registrar or domain provider. A reliable result identifies the domain, its availability status and the time the provider checked it. An unavailable result may mean the name is registered; a query error or unsupported extension is inconclusive, not proof that it is taken.
Check price separately from availability. Providers can return registration, renewal and premium prices, and promotions can affect the initial amount. Compare prices in the same currency. Missing price information is not a zero-dollar offer.
Availability is a point-in-time signal. Someone else may register a domain after your check, so confirm again with the registrar at checkout. A domain being available does not mean the matching name is available as a trademark, company name or social handle.
Keep a record of the exact spelling, extension, provider and check time. That makes it easier to compare candidates while remembering that the registrar's final result controls a purchase.