Map the Basic Layout
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Measure the room with measuring tape and make note of the dimensions.
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Based on the room's size, design a legend with appropriate scale (for example, one one-inch grid equals one foot). The larger the room, the larger the scale will be.
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Using the ruler and pencil, plot out the walls of your room on the graph paper. If necessary, use a larger scale or tape two pieces of graph paper together.
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Add windows and doors to your map. Measure the window or door's width and distance from the closest perpendicular wall for accurate placing.
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If your room has any other stationary features (counters, sinks, in-wall oven), add them to your map in the same way as doors and windows.
Add Furniture Cut-Outs
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Measure the length and width of each piece of furniture.
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On a separate sheet of graph paper, draw each piece of furniture to scale. Be sure to use the same size grid and the same scale as your room map.
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Label each piece of furniture on the graph paper ("sofa," "bookshelf," etc).
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Cut out each piece of furniture.
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Place the furniture cut-outs onto your original map. You now have an accurate map of the room. Slide the furniture cut-outs around the map to try different arrangements and see what will fit where.
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If you're considering buying new furniture, find the dimensions and make a cut-out of the new furniture to see how you can incorporate it into your room.