Great question! There are actually a number of resources out there that answer this question. Here is a very dry (but unbiased) answer from the Canadian Paediatric Society written for paediatricians who are helping parents with this issue.
Here are some quick question to ask yourself when appraising the website you're looking at:
1) Most importantly, whose website is it? The most reliable are generally university or health agency websites. Next would be not-for-profit professional organizations (for example the American Academy of Cancer Researchers or the American Medical Association). Be wary of for-profit organizations and websites run by one individual or a small group of individuals.
2) Is the information referenced and peer reviewed? An unreferenced statement is useless. Even if it's referenced, the reference should ideally point to the peer reviewed literature, not to a secondary source (such as a news site).
3) Is the website itself peer reviewed? This isn't mandatory but it helps you have trust in the website.
If you have the background you can go to the references and evaluate the literature itself - is the population described relevant to you? Was the intervention what you were looking for? This is advanced and probably unnecessary if you follow the other rules (especially number 1).
The bottom line is that reputable organizations are likely to have accurate information. The NIH, CDC, or Mayo Clinic will always be more reliable than a single person's website (no matter who they are). Look for .gov or .edu at the end of the URL - these are reasonable indicators that the information has at least been vetted by more than one person.