How to add extra css in style.css file? I want to add extra css for my images (I just want to set float:left to them).

I've checked where I need to add my CSS i.e.&lt;div class="field field-name-field-gallery field-type-image field-label-above"&gt;.

So should I directly add this class name in style.css file or should it go somewhere else?
Yes, if style.css is a CSS file that's loaded into your page (either by a module or, more likely, your theme) then that's probably a good place for your custom styles.

If you'd rather have your own file for custom styles though, you can just create a file (e.g. custom.css) in your theme folder, and add a line like this to the theme's .info file:

stylesheets[all][] = custom.css


Once you clear Drupal's caches you should see the new stylesheet included in all pages using that theme.