How to make styrofoam look like wood

First, get a piece of styrofoam. I typically buy mine in 4ft by 8ft pieces in the insulation section of Home Depot or Lowes.  It comes in 1/2 inch or 3/4 inch at my stores.  Some places I have found sell them in 2 inch thick sheets.
This is a 1/2 inch thick piece of pink foam.  The blue foam is the same
but the regular white styrofoam doesn't work well for this.
The pink/blue foam is far denser than the white stuff.
Cut it to the size you want the final piece to be.  You don't need to cut each individual slat, just the finished piece.  I am making the background for a sign, so this piece is about 2 feet wide and 3 1/2 feet long.

The thing you need to remember is ALWAYS REMOVE THE PLASTIC SHEET! If you don't then you will end up with a huge mess that won't accept paint.  I like to peel the sheet off of both sides but that is just me.  It does need to be off of the front at least.

Next use a wire brush and rake it down in the direction you want the grain to run.  Dont go in different directions or it won't work. You can use the brush sideways or straight.  I typically start in the middle of the board and pull all the way down to the edge.  You are going to think "I am doing this wrong.  It is messing up."  Don't Panic (Hitchiker's Guide to the Galaxy reference there.) It is supposed to look messed up.  Keep going over the same spot until you reach the depth you want.  Do this across the whole surface.  Make sure you keep going past the edges too.

You will be left with a deeply scarred piece of foam.  Now if you want to make planks or what looks like different boards just go deeper with the wire brush in the "crack" areas. You can tilt the wire brush sideways so only a little bit hits the board or you can use a small wire brush (one that looks like a toothbrush) to make the "cracks."  

Next use a paintbrush to sweep away the extra bits that are left over.  I have found that brushes that are no longer good for painting are usually good for this part.

Now it is time to paint.

You will want to use latex paint on this, not spray paint or it will end up being eaten away by the spray paint. I started off with a medium colored brown paint. (I used the Apple Barrel kind on this one.)  I poured it in small amounts all over the styro.  I also use a spray bottle of water to thin it out a little.

While it is still wet, spray it with some water and drip darker colored paint in random spots.  I used a burgundy, dark brown and even black.
The trick is to keep it wet.  Run the paint brush with the grain, and mix the paint on the board itself.

If you are making planks, then make the "crack" areas darker.  

It ends up looking something like this.  Stand it on one end and let it dry.  The paint will run down and puddle so make sure you have a tarp down or it is somewhere that can get paint on it. Make sure you stand it on an end so the paint runs with the grain.  You wouldn't want the paint to drip across the grain then it wouldn't look right.

Here is another one that I have done. The wood is darker in this one.

You might notice in the bottom left corner there is a knot.  I used a tiny heat knife to do this before I painted it.  I did it in a few other areas too but those are harder to see in this photo.