You will certainly need a telephone (or two), even if you use a cell phone much of the time. It is still necessary to have a landline phone, because you can't send a fax via a cell phone.
You will need to write and answer emails in your home office, so you'll need the right facilities to do this -- a good computer with broadband for speed, if possible. What you do in your office depends on the business you have. If you need to pack and post items, then you will need table space apart from your computer to do this. You may even need to display and/or store products, so you will need the correct storage.
If you need to draft plans or make patterns, then you may need to expand your workspace rather than someone like a freelance writer who is at the computer most of the day.
A home office is also used for keeping records, and you may keep personal records as well as work records here. You'll need a good-sized filing cabinet for this basic function and maybe other shelves or drawer space. You may prefer to keep personal records in a separate filing cabinet for privacy.
You may have to interview or meet with people associated with your business, so your office will function as a meeting place. It's a good idea to have outside access to your office, and then you won't have to bring clients or customers through the rest of the house to get to the office. They won't be all that impressed with the baby screaming and kids' toys all over the floor.
You will need enough comfortable seating to deal with your clients, as your home office may function as an interview room. Are you likely to have one client waiting while you deal with another? Then you may need a small waiting room close by - you could even have tea or coffee making facilities in it.
You have many places to set up a home office. The location will depend on your own circumstances. It may also depend on whether you need a private and personal office or one more orientated towards family use. What you intend to do in your office will also have some bearing on its position. If you only need space for a computer desk, then it will be easier to find a suitable spot than if you also need other tables.
You could install a family office in the family room or whatever you consider as the main room of your house. This way you can do what you need to do without isolating yourself from the rest of the family. You may need to rearrange the furniture so you can fit your computer desk and assorted paraphernalia along one wall, or part of a wall.
If your family room is large enough and one wall is an external wall, you may consider dividing the room with a properly built wall, then you could have outside access if necessary. If you don't need outside access, then you could arrange the furniture to create a division.
Under the stairs is another space that is often under-utilized. With proper lighting, it could become your new office space. Shelving could be installed under the lowest part so you don't bump your head on it.
You may have a spare bedroom you could utilize -- or even a small storeroom, an awkward corner somewhere, or you could block off the end of a hall. To make more room in a smaller bedroom that holds two single beds, you could have bunk beds instead. If you don't need two beds in it, then a futon or folding sofa bed might be an alternative. This would free up enough space to hold a computer desk.
Some creative people use the space of a built-in wardrobe room to fit their home office into. The advantage is you can close it off when you are not using it and it is not intrusive. Nor is it a tempting to young kids. The room will look much tidier, too.
Other possibilities include the attic or the basement. Very often the space in these two rooms is not utilized at all, but kept for storage. If you decide on the attic, you may need to get a builder's advice about strengthening the floor and see about lighting and heating, while the basement may need professional treatment for dampness...
