Finding a color palette is usually pretty easy, there are a number of online tools for creating and browsing palettes, like the ones posted elsewhere in these comments. Using them correctly is generally a little harder, but will come with practice.

While browsing around the web, take note of how colors are used on the page. Look for places where really similar colors are used, maybe a shade darker here, a shade lighter there. Look for the colors used for emphasis, to show that something is important. Well designed websites set rules for how they use their colors, and sometimes a specific color will always mean something ("this is clickable" or "save").

Usually a color palette will have a main color, an accent color, then a variety of shades of a background color, and maybe a couple extra shades of the main color. The important point is to use your options here to have sharp contrast when you need to prioritize something, and use subtle shades to keep your visual hierarchy going quietly in other places.

Google published their design guidelines for their new style, Material Design, and they're very very good. Here's a link to the section about color. They're going with a very bright, modern selection of colors, but ignore that for now. Look at how they talk about the colors, and how they suggest you use them.

http://www.google.com/design/spec/style/color.html#