Step 1: Create Your File.
The first two parts of this can be done in any paint program. Save the result, and import it into Inkscape.Select it, and under the "Path" menu choose "Trace Bitmap." Select the "colors" radio button and adjust the "steps" option to 2. You will now have an additional object sitting on top of what you imported. In creating it, Inkscape will have done a good job of adapting the shape into vector form so you can scale it smoothly, as well as converting "really dark" and "really light" into one color each. Ungroup that (under the "Object" menu) and drag the two pieces of it apart. One of them is the dark shape you want to print; the other is going to be a light-colored box, which you can delete.
Delete the original imported version of your image, leaving only the vectorized thing you want. Adjust the fill color on that part to be black. Re-scale the paper to fit the drawing (Inkscape has a button to do this automatically under "File" > "Document Properties"), then add a box around it that has the same proportions as the image, no fill paint, and a stroke width of .001". Save your file.
Step 2: Cut Your Woodblock
You're going to be using the laser to raster etch away everything that's black in the image. Put a piece of plywood in the laser, and cut/etch it using the settings you prefer on your laser for that wood, at slightly lower speed to remove more material. (It may well work best to etch it again and go deeper; ideally you'd like to go almost a sixteenth of an inch into the wood.)
The box you drew around the raster image will cut out the block, as well, so you don't have to etch away the entire piece of plywood of whatever size.
Usually when making woodblock prints, hardwood is your best bet. It'll last a bit longer than soft woods and you can get better edge definition. With the laser, you'll get crisp edges regardless of what wood you use, though hardwood will still be more durable. I just use whatever plywood is cheap.
Step 3: Make Your Print
Put a little bit of ink on the ink plate and roll it around. Roll the roller back and forth on it both ways until it is evenly coated with ink. Then, roll it over the etched surface of the block. Don't roll it back and forth on the block, since over-inking will fill in the etched gaps in the design. A bit of practice and you'll get a feel for how much ink to apply; it should be just enough that the entire raised surface is inky and sticky.
Then, flip the block over onto a piece of paper and press down firmly on all parts of the wood. I then like to trace around the outside of the block so I can trim the paper to size afterwards; this is far easier for me than printing on a correctly-sized piece of paper to begin with, as I don't always get it exactly square with the sides of the paper. Then, lift the block straight up off the page; what's left behind is a print. Give it a while to dry, and show off your handiwork.