If your room size is restricted then the answer to your problem lies in stairs for small spaces; there are numerous models today that offer high quality design and warmth to the living space, as they combine the warm shades of wood with modern elements and many space saving options and details.
Stairs can be quite hard when it comes to integrating them to small spaces; you can choose to make them float in the center of the space, using the space on the sides and underneath, or taking advantage from the lack of surrounding walls. This is a trick implemented in many houses that lack space; the second level always looks bigger and taller than the one of similar houses, just because of the smart interior design and planning.
Whether you opt for floating stairs for small spaces or not, the useful area around them is rather limited, thus, you can choose to place them in a corner or against a wall, if you wish to take advantage of corners and shadowed spaces, opening up more floor space. For those who wish to add a more urban note to their space, there is always the option of aluminum alternating tread unites which are becoming very popular lately, due to their ultra sleek design and the space saving concept. For some people it might be too narrow, but it combines style and practicality and can be used anywhere, from the attic to top floor or from ground floor to basement.
Stairs for small spaces might also come with a railing system that anchors them anywhere you might want; this type is quite adjustable in height and solid enough to ensure safety even if you have small kids around.