Once you understand the type of work you will be doing and the kind of space needed to support that work you can start looking around your house or apartment to see what you have that will be suitable.
Your own bedroom may be a possible choice since it will normally be unused during the day time however, if you will be working late into the night, this may present issues for your spouse. And, of course, waking up directly to unfished work may not be the most pleasant way to approach the new day. If you do place your offic in your own bedroom consider some way to screen off your work area from your sleeping area.
A spare bedroom, or even a large, empty, walk-in closet, is an ideal place for an office as long as you do not receive visitors on a regular basis. If your office is too small, or not suitably situated, to receive visitors at all you can always take your business visitors to your living room, kitchen table or even meet them at a local coffee shop when necessary.
An attic may offer interesting possibilities for an office. Renovations may be required but it is still worth considering. Be sure there is suitable electrical service for your computer and other equipment and, of course, enough light.
The basement is another place to look. If your basement is unfinished it may also require some renovating. You will need to consider potential problems due to dampness, if any, as this can cause serious issues with electrical equipment, papers and even your furniture. A dehumidifier may need to be added to your equipment list.
It's never the best choice to place your office space in another regularly used room but if all other choices fail you may consider putting your office space in the corner of a family room or even your kitchen. You can paint your office furniture (desk, file cabinets, etc.) to match the room decor but there is little you can do about the distraction others using the rest of the room may cause. A lot will depend on your normal living style and how your home based business fits into this. If you have children you will need to establish ground rules for access when you are working.