By default, Safari comes up showing a page of icons of your Favorites. You can add to this by going to the site you are interested in and make it a favorite. Use control-D and save a bookmark into the folder "Favorites" using the listbox at the top of the dialog box that appeared.
If you have set a different default site for Safari, you can click on the "Show Top Sites" icon in the Safari Toolbar (by default near the top left). You will see either "Favorites" or "Top Sites" at the top of the page but under the Toolbar. If you don't see "Favorites", look at the top right of this page and click on the box containing an asterisk '*' on one side and an array of 12 dots on the other. Click on the asterisk to show the favorites. The "dots" side will display the "Top Sites" or your most used sites.
You can arrange these icons as you want by dragging them into place. They can be edited by right-clicking on them or using control-click if right-clickiing is not enabled in your Settings Mouse configuration. A small drop-down list will offer options for editing.
Another option is to left-click on the URL and drag it to the desktop, but a lot of files on the desktop both clutter it and can actually cause OS X to lag - slow down. Many Windows users, as you said use a technique similar to this, but I don't recommend it on the Mac.
I hope that this is helpful.
Trauts