How long does it take for changes to my website to appear in Google?

It depends...

Generally, the more frequently you add content to your website, the more frequently your site will be re-indexed by Google.

If you add content to your site every day I would normally expect new content to appear in Google's results with 48 hours, and changes to content should also appear within a week or so.

Similarly websites that lie dormant for some time end up being largely ignored.

Tips

Blogs, (web-logs), can be useful, (if they are published on your website rather than on a 3rd-party site like Blogger.com), as they encourage new content to be published on a fairly regular basis. Even better than blogs though is the practice of adding original and useful content that your target audience might find useful if they were to find it via an online search.

Links are essential for new websites to help Google's robot, (Googebot), find your website, and a site-map is recommended to help Googlebot find all of your content and to give Google an idea of your website's hierarchy.