Maybe you have more important things to do, like focus on your business, instead of managing your website. Maybe you don't know how to manage it, and maybe you just don't want to. Whatever the case is, be sure to take a few points into consideration before hiring someone to manage your website.
Find out what the web person's reliability is. I often work with graphic artists while building web sites for people. Some graphic artists are prompt and very reliable. Some graphic designers I've worked with disappear for weeks on end with no notice. Since vices and virtues are distributed amongst all people, not just graphic designers, determine the reliability of your web person before you hire them. How can you do this? Ask for references. Call those references and ask them questions. Try to be specific. It's okay to ask "Do you feel this person is reliable?" but try to ask some less vague questions too. "What was this person's response time to you on average? What was his fastest response time, and what was his slowest response time?"
Does the web person have the time to take you on as a client? When can he or she fit you in? Does that work with your schedule? Can you wait until that person is available?
Many types of web sites exist. There are the flat websites which are like brochures on the web. There are more complex web sites made of content management systems (CMS). Some of those content management systems are common and many people know them, but others are rare. Additionally, some systems are custom-built, and the sites can be written in different languages. If your web site is already built and you are looking for someone to maintain it, make sure the person you hire can actually do the work. (If you don't know how your web site was built, hire someone just to figure it out the requirements a we maintenance person needs.)
Verify this person's ability. Besides just talking to past clients, ask for some web site URLs and peruse the sites.
Talk to the person and see if your personalities work together. If you must talk on the phone with someone and the web designer hates the phone and strictly uses email, no matter how good that person is, you'll be frustrated. Personality traits to consider include: communication preferences, hours kept, and how much control you need versus how much independence the web person needs.
In my opinion, cost is the least important factor. There are some fantastic engineers in third world countries that I have enjoyed working with. However, there's the potential of communication difficulties, time zone difficulties, and cultural difficulties that might make the less expensive cost not worth the extra time and effort the project takes. If someone charges one-third the price but takes three times as long to finish the project, what's the point of using the less expensive person?
Where can you find someone to manage your web site?
There are a lot of great places to look. Besides the traditional ad in the newspaper, you can use many online sites. After all, you don't necessarily need to have face-to-face meetings with your web maintenance person.
PeoplePerHour.com is mostly an European site, but not entirely. For some reason, I love the way this site works.
IVAA.net is the International Virtual Assistant Association. Some of the members of this group are technical virtual assistants who can maintain sites. Web designers and programmers also join IVAA, so it's worth your time to look there.
Also, some common places to look are elance.com and guru.com.