Decide how you will make use of the short arm of the room's L shape. Dodge the challenge of integrating a spatially isolated section of the room into the main axis of the room by making its isolation a virtue. For example, use it as a home office area, a library, the kids' homework spot, a crafting nook or even a yoga niche.
Draw two representations of the living room to scale on graph paper. One representation should depict the long axis of the L -- the main area of the room -- while the other should depict the short arm of the L.
Make paper representations of each of the major furniture pieces and other items you want to include in the living room. For example, account for a sofa, a recliner, an entertainment system, a television, a coffee table, side tables, lamps, bookshelves, a desk, a yoga or stretching space and toy storage. Even if you don't know the precise dimensions of the sofa you will purchase, make an educated guess, and cut the paper model to match that size.
Cluster the furniture items associated with the use you chose for the short arm of the L on that drawing. Move them around, and look at whether you can incorporate other items into the space. This helps ensure that the long arm of the L isn't too cluttered. Remember that furniture and functions can be stacked vertically. For example, if you opt to make the short arm into the family blogging nook, you can add storage space by installing shelves above the computer.
Arrange the remaining furniture paper pieces on the drawing of the long arm of the L. Prioritize placement of these pieces by how you actually spend your time in that part of the room. For example, if you spend most of your living room time sprawled on the couch reading a book and glancing out the window at the bird feeders, situate the couch first to maximize natural reading light and the bird feeder view.