I've seen so many pretty cakes with the board covered with fondant and I want to try it, but don't have a clue how to do it. Can anyone on the great site help me out? Thanks!

I don't have a site/video link for you but I have done it and it is pretty easy. I use sturdy board. I have used mirror, masonite, and foamcore over masonite for thickness and all have worked.
Roll out your fondant to an even thickness less then 1/4 inch-what you are comfortable rolling and working with. Roll fondant a coupple inches bigger then your board. Stlightly moisten your board. I use a damp towel to barely moisten the board. Lay your fondant onto your board. Smooth your fondant flat onto the board with your fondant smoother. Use a smoother to go around the edge of your board at about a 45' angle. Around and around and around. It will cut the fondant exactly to your board and smooth the edge at the same time. Trim edge of board with ribbon...ect And you are ready to lay your cake on it. Use a bit of icing to glue your cake to the fondant surface.

I use even the drums for cakes, wet them and roll the fondant just like I would for a cake. Put on the board and cut the sides
Edna

I do it a little bit differently...I use foamcore and I roll the fondant directly on the dry foamcore board. Just roll to the edges of the board and off a little bit, and as the rolling pin goes past the board it smooths and trims the edge. Then glue a ribbon around the edge when you're done.

You can also use stamps to make impressions on the fondant...rubber stamps mounted on wood are not food safe, but my cake goes on another board on top of the decorated board, so I figure it's all right to use them on the cake board. Here's an example, where I used stamps and then painted over the impressions with silver airbrush color (with a paintbrush, I don't have an airbrush)

Ok, thanks to everyone! I think I get it now I still do my cakes with buttercream, so can I put that onto a fondant board, or should I try a fondant cake for that?

You can put a buttercream cake on a fondant board.

I have done it in buttercream too..Let it dry well..
Edna

Just as a quick tip, since the PP's did a great job of explaining how to get a smooth surface, I like using RI for the board too. If you make your RI a flooding consistancy, I place my board on a cooling rack over the sink and pour the icing on top of my board and then spread it around with a spatula. Allow to dry for a couple of days and it is as hard as a rock. Perfectly smooth, and ready for any kind of cake to go on top.

If you want to re-use the board, a parchement paper round underneath the RI will allow you to remove the RI without damaging the board or chipping away at it forever.

Ok, then I will give it a try with buttercream. And, wow, who would have thought to use royal icing!!? I would think that would be great also. I've wondered how far ahead to cover the board with fondant, because if you didn't let it dry some, anything that touched it, including fingers, would mark it all to pieces.