What types of customers have you worked with?
The most common types of projects I do are simple, clean, mainly informational websites with high visual appeal and tasteful use of modern browser technology; print design of brochures, business cards, newsletters, etc.; and brand design. But this is by no means all I'm capable of... let's chat!
What advice would you give a customer looking to hire a provider in your area of work?
Make sure your provider knows the fine details of their trade... which means you'll have to know a little bit about it yourself. It's easy for a person to say, "I make websites," but how are they going to do it? Will they use an off-the-shelf software package but don't actually know how to write code? If they do write code, do they follow best practices, use version control, make backups, document their code, etc.? You might only need a simple site now, but if down the road you switch designers or need additional functionality, you want to make sure you won't have to start from scratch.
Likewise, there are lots of sub-disciplines within design, one of the most important being design for print. The rules are different between print and screen, and you want to make sure the person you're hiring knows about bleeds, CMYK color conversion, spot plates, imposition, etc. It can save you major headaches once you take their files to the printer.
If there was one last thing I'd mention, it's that you get what you pay for with design and web. Anyone with a copy of Photoshop can theoretically make a website or a logo, but the quality may suffer. Your brand collateral is your contact with your customers, so always put your best foot forward.