Testing how your website looks and performs on a mobile browser usually requires you to buy the appropriate hardware. It can be expensive, and doesn't make for the most convenient testing environment - but fortunately there's a simpler alternative.
Opera Mobile Emulator is a version of Opera Mobile 10 that's available for Windows, Linux and the Mac, and downloading and installing it will let you view your site (and anything else you like) as though you were using a mobile.
Once you're at a page you can scroll around, zoom in and out, follow links, and generally behave just like any other visitor. You're able to tweak various browser settings to see what effects they might have ("Load images", "Opera Turbo", "Opera Link", Fullscreen", and so on). And you can even set different user agents, if your pages check for these (the options available are "Default", "S60", "Windows Mobile" and "Android"), quickly revealing how your site will respond to various devices.
The program also comes with an Opera Widgets Mobile Emulator, which does a very similar job, displaying Opera widgets in a mobile-type form factor. Launch the emulator and you're able to load and test widgets just as you would on a Symbian or Windows Mobile device.