IANAD, but...
Take zinc and vitamin c supplements starting immediately. When you feel symptoms that are definitely consistent with a cold (running/stuffed nose, frequent cough or sneezing, post-nasal drip, etc.), begin taking, in the daytime, pseudoephedrine or other epinephrine-simulating drugs (Sudafed is the most common) and dextromethorphan (which is a cough suppressant), with perhaps an antihistamine (such as Benadryl). Dayquil combines these. At night, the best is probably Nyquil. Do not exceed the recommended dosage or mix drugs where the label warns against it.
Also, once you begin coughing, menthol-based cough drops are the best choice, as is something somewhat sugary that can help to coat your throat with its syrup. Halls or Ricola are good, but I find Fisherman's Friend works the best, although it is VERY strongly mentholated.
This will most likely not shorten the duration of your cold. It will, however, treat the symptoms and allow you to feel better and operate more normally.