Since it is impossible to literally build and attach another room, reorganization of your existing space is the key. For example a garage could be successfully converted to another room, or there is an option to relocate your kitchen to the basement and use newly freed precious space for whatever is necessary and more important to you.
There are certain tricks that can serve as space savers:
paint a room in a lighter shadow gives that light and airy feeling and instantly expands the space, fold up furniture which is very practical and can be stored away while not needed, simple and light window drapers and mirrors which reflection will widen the space.
Its only helpful to carefully plan furniture arrangement, even if you want just only move around that sofa and that dining table. Putting plan on paper will save you enormous actual moving effort, provide you with understanding of items you need to purchase and give you an idea of final look.Carefully measuring your room dimensions is important when buying new furniture. Dont forget to include doors, windows, pillars and fireplace in your sketch. Measure everything carefully. It is pivotal when ordering custom made furniture, I doubt a building company will take it back if you failed to measure,
There is one visual tool. You can accurately draw the sketch of your room, then on a separate piece of paper draw shapes of pieces of furniture (owned or planned to buy) , cut these shapes out and then move them around on your room sketch. Just bear in mind that these furniture shapes must be on the same scale as your room dimensions!