First off, welcome! One of the best things you can do is use your tutorials. Almost all new Mac apps have tutorials and most of them are pretty good. There's also a wealth of knowledge to be had here just perusing the forums. If you need help with anything specific, just ask. Also, you may get a little more in the ways of tips and tricks if you tell us what kind of Mac you're using and which OS.
My suggestion for anyone first coming over to a Mac is to by Little Snitch after you get used to how the Mac OS works. Little Snitch keeps track of all outgoing signals from your computer. You can set it to block the ones you see fit. Worth the $30 for peace of mind.
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