Surface applications are not too difficult to apply, but opening the stairway means reframing or rebuilding the stair. That would exceed the expertise of most homeowners. Your question is not specific enough to help you, although I can fairly well picture the enclosed stair. My guess is there is another stair above the one from the first floor. If any walls are an outside wall, you could consider installing a window to give more light and openness to the stairway. Opening could also be framed into other rooms next to the stair giving an open view from the stair. Any modification must preserve the structural integrity of support walls. It can be done, but you should consult professionals if your experience with framing and structures is limited.