Hiring employees at a start-up is probably the most important step of any business's growth.
The people you hire are the eyes, ears, hands, and mouth of the company. They will create the products and perform the services, listen for feedback and customer complaints, respond to problems and more. They're the people who sell, and everyone from the receptionist to the stock clerk has the potential to connect with your customers in a positive or negative way.
In addition to thinking about employees as the key parts of a company, it is important to think about team dynamics. Make sure that you hire people you want to work with, and who believe in the vision of your company. There's an old saying that "A people hire A people, and B people hire C people." If you hire the best people, when it's their job to hire, they'll also hire great people. Dennis Crowley of Foursquare recently spoke on the challenges of being a CEO. He spoke about hiring a programmer, and eventually promoting him. The programmer then had to realize that he could spend a week fixing a problem, or spend a few days and hire people who were better at the problem to code for him. If you teach employees to hire for great skills and not to be afraid to hire people better than them, you'll constantly improve your company with each hire.
The legal aspects of hiring are many and varied. It's important to know the restricted information you can't ask in a job interview (things like race, height, weight, and more.) This piece called "Don't ask an applicant these questions" does a good job of summarizing, but a chat with your attorney is a good idea. These issues should be discussed with other employees, board members, or advisors if they're helping you vet candidates since anyone acting on your behalf could open you to a legal issue.
That brings up another point - don't "improv" in a job interview. You should know the questions you want to ask, and how you want to ask them, before a candidate arrives. If you're being deliberate and have a list of qualifications, qualities, and skills you want in an employee, writing them down first is critical. Have a mentor, advisor, lawyer or other trusted person look over your list.