Work with the room you have
Look for a place where you can sit comfortably and put down anything you need. It might be a chair by a window, the end of a table or a space that has another use during the day. You do not need a separate room.
Notice practical details such as glare, noise, temperature and whether you can reach a light. Small adjustments to what is already there may be more useful than replacing the furniture.
Keep the purpose clear
Decide what you would like to do in this place: read, listen to something, talk or spend a few minutes quietly. Keep the items for that activity nearby and move aside things that make the space harder to use.
In a shared home, discuss when and how the space can be used. A simple agreement about a chair or a short period of quiet can make a modest arrangement workable.
Allow the space to change
Your needs may be different across seasons and schedules. Move a lamp, change the time you sit there or choose another place when it suits you. The point is to have a usable space, not to maintain a perfect-looking corner.