They should absolutely have a website of their own and that website should work. Every page you go to should work really well and should load quickly. They should have a lot of work on there that is represented well and shown in full and links to other websites that they designed. Often times they will have testimonials or referrals from other clients right on their website. A lot of them will also offer the names and phone numbers of some of their referrals for you to check and make sure that they are dependable and that they answer e-mails and phone calls and that they will do the work in the set amount of time. It's important for a web designer to sign a contract with a client but it's also important for the clients or customers to get a contract signed between themselves and the web designer. The majority of problems and complaints that I see stem from people who did not have a contract or agreement or they had one but it wasn't really good. If you are hiring a web designer and they are not professional enough to sign a contract or create one themselves, it's probably not somebody you want to deal with anyway. Anytime you're doing business with somebody who might not be right in your own town, you definitely want to make sure that there is a clear agreement about what's going to be happening.