Styrofoam can be purchased in nearly any size. If you are fortunate enough to live in a city that has a foam wholesaler you may even be able to get it in one piece. Styrofoam panels, the type used in insulation, are cut from much larger Styrofoam block. A foam company that cuts its own foam can custom cut almost any size and shape and may be able to cut the beam, including wood grain detail, for you.
No foam wholesaler in your area? Your local home center should carry 2-inch Styrofoam insulation in 4-by-8-foot panels. Cut strips the correct width and length and glue them together to form the height of the beam using latex liquid nails (available alongside caulking and adhesives at lumber yards and home centers).
Whatever form your foam takes, measure your space to determine how much you'll need. Once you have your foam, glue it up or cut it down to form a beam.
Styrofoam can be sculpted using almost any tool with a cutting edge. If a professional hot knife is available it is the best bet for long, smooth cuts and precise notches. A few tools that work well with Styrofoam include an electric chainsaw for large, rough textured cuts; electric carving knives for smaller, semi-precise cuts; any power saw or router; and a Dremel tool for the fine detail you'll be wanting.
Study a piece of actual wood like that you are representing. Different types of wood have varied textures. Remember that wood is an organic material and the grain of it was once a living thing. Keep your tool moving and avoid square corners and long straight lines for best results.
Once you've completed the carving, cover it in cheese cloth to give it an earthy feel. Mix two parts latex paint with one part glue. Cut cheesecloth into 10-inch swatches and paste it on using the paint/glue mixture and a brush you don't mind destroying. Make sure to get it into the details. Add as many coats of glue/paint on top as needed to get the look you want. You can add a water-based clear varnish to add sheen.
Locate the ceiling joists or wall studs to anchor a wooden base plate to. Use a circular saw to cut a piece of 1-by-8-inch lumber to the length of the beam. Paint the edges of the board to the color your beam will be and allow to dry. Attach the board to the ceiling or wall with a drill and screws, making sure to get your screws into the wall studs or ceiling joists.
Attach your beam to your base board with more latex liquid nails. Reinforce it with a 3-inch screw about every 2 feet on each side. Angle the screws through the corner of the foam into the base board about 2 inches out from the wall or ceiling. Run your screw just below the surface.