Computer (mac) question

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I've made the move to Mac from pc. One of the things I could do on Windows was grab a pic off the internet and send it to a thumbnailed folder where I could access it at any time. Can anyone tell me how to do that on a Mac, cause I can't figure it out. When I grab a photo they become (i think) linked files. In other words I can see my pics when I'm on line but not if I'm offline. How can i capture, save and, when offline, access a pic. I could do this easily on Windows but can't figure it out on the Mac (OS X panther). Can photos from the web be stored and thumbnailed in Documents?? Thanks in advance for any help.