When affixing wood to concrete, one of the best, and easiest, methods is to glue the wood to the concrete with epoxy. One suggested glue is PL-400. It comes in a caulking tube and is sold at almost all hardware stores and lumberyards. Gluing the wood to the concrete is faster and easier than drilling holes in the concrete for lag bolts or using explosive nails to affix the wood to the concrete.
Place the PL-400 in the caulking gun and cut off the tip of the caulking tube, opening a 1/8 to 1/4 inch diameter hole.
Make sure that your wood is exactly the size and shape that you want it to be. Once you glue it down, you will not be able to move it.
Make sure the area is clean of debris.
Apply a generous amount of adhesive to the wood and put the wood in place. Firmly press the wood to the concrete. If the wood is on a floor, place some heavy weights on top to maintain pressure. If the wood is on a wall or otherwise not lying flat, use clamps.