Try a crumb coat. I ususally just thin down my regular buttercream and do a very thin coat on the whole cake (you should see your cake through the icing) There is no reason to be neat about it. Wait for it to crust, about 10-20 minutes, then put on your final coat of icing. Also dont let your spatula touch the cake. If you do get crumbs on your spatula, dont dip it back into your icing. Once they are all in the icing it is hard to get them out. Make sure your final coat of icing is thick enough too.
traditional method: crumb coat...a thin layer of icing put on cake and allowed to crust over (harden) must use cursting buttercream frosting. then after it is harden, the final coat of icing is applied.
the "I'm in a hurry and need to get it done now" method. Use tip #789 the "cake icer" tip...very large tip that is used w/ large bag (16" or 18"+) and lays down a layer of icing about 1/4 inch thick and almost 2 inches wide. (i usually use this...too impatient for the other) look see at this site:
http://www.wilton.com/store/site/product.cfm?id=3E30C1CD-475A-BAC0-5CDB07AA69762110&fid=3E3324A4-475A-BAC0-5ED544474B973201
Welcome to CC! It takes lots of practice to avoid crumbs, but having your icing thin enough to spread easily helps. Also, make sure it is laid on thick enough so that when you smooth it with your spatula, it doesn't pull away from the cake. I've read here that dipping your (metal)spatula in hot water can help smooth too. Good luck and remember, mistakes can be eaten!
If your cake is frozen or cold, it helps, you can brush the crumbs off easier, then do the icing.
Welcome to CC, rfonte2! You are gonna love it here! Congrats on your first cake!
Good Luck in the future! 
Anna
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