This is a great question because it is applicable to most parents and the answer varies dramatically depending upon individual circumstances. Depending upon the location of the office, the contents and how you wish to use it dictates whether a very simple $5 solution or a more complicated $500 solution is appropriate.
Some of the hazards of which to be aware of in a home office include the electrical outlets and power strips, cords from telephones, computers and window treatments, bookcases, paper shredders and paper cutters. Note, the expanding prevalence of paper shredders is resulting in an increasing number of children requiring amputations from having their fingers pulled into the machines.
Since there are so many issues to address in a home office, it is often easiest to make it an "off-limits" area by latching the door closed. Many parents, however, want to hear and see their children while working in the office; installing a gate in the doorway can accomplish this. For those who want their little ones closer, but not too close, a gate that surrounds the workstation is another option (Note, the KidCo ConfigureGate works well for this application).
If you don’t wish to be barricaded in your office, you will then want to address the safety issues I referenced above. Place outlet covers (box type) over the electrical outlets and power strip covers over the power strips. Use cord conduit to conceal exposed cords and wires running along floors and walls. To conceal the tangled nest of wires behind the computer, create a false back to the desk with a sheet of plywood or cardboard slid between the desk and the wall. The sheet will conceal the wires from your child’s vantage point and not impede your access to them from above. Install cord cleats to keep your window cords secured out of reach. Brace your bookcases to the wall to prevent toppling from earthquake or a climbing toddler. Unplug the paper shredder when not in use and never allow your children to feed paper into it. Finally keep your paper cutter and any other hazardous items up and out of reach.
As you can see, there are many issues but also many options as to how to babyproof your home office. First determine how you wish to use the space, then make the necessary modifications. Be aware, however, that as your child grows you may progress from one stage of access to another, so you may use many of the strategies and tips listed above before you are through.