Bringing all of the elements of a beautiful living room together is really quite formulaic. First one should choose the sofa, considering the size of the room and intended use. Once that has been chosen, select a rug which contrasts or compelements the sofa. I think its always a good idea to have the largest pieces in a neutral color scheme and add some trendy items for for accent pieces.
Once those pieces are chosen, then an arm chair or two are usually enough to fill the space, or perhaps a love seat. These are usually in at least one tone of color from the couch, with perhaps a contrasting shade or pattern. I think it looks nice to have each piece in the room a bit different for interest, but some will match at least two of three pieces.
Once the rug and furniture have been placed, then the need for tables will become apparent. Side tables are nice along an empty wall space. An end table or ottoman should be available near each sitting location to place a drink on. Some couches come with an ottoman which can be used as a coffee table, with the addition of a tray if needed. Many end tables can also double as extra seating when required, such as the cube style wooden or wicker storage tables or ceramic stools which are available.
After that its just the fun of adding a few accent pieces like vases or pillows, often with a nice pop of color, to liven up the space!