If a sim is just coming down with the symptoms, sometimes a nap, orange juice or healthy green tea can ward off the illness. If that doesn't work, they will often get the whim to take medicine to combat the illness. Click on the computer and click on 'Order...". There you will find the option to order medicine. Once purchased, have them drink it (will be in the personal inventory of the person that ordered it). This seems to cure everything.
As a precaution, I often have the kids in my household use two of the Have a Quick Meal options at breakfast: Orange Juice and Cereal. For the adults, Healthy Green tea and cereal or yogurt. I've had a lot less incidents of sickness since I started doing this. Before, it seemed someone was always sick in the house (full 8 sim household). Since they fixed the eating/drinking interactions so they don't pause SO long, my kids can easily have their cereal and drink their juice before school.
If you pick two Have a Quick Meal options (like juice and cereal), the sim will get the first one from the fridge, sit down, and then get up for the second item and then will eat/drink both (which I love - especially now that it's fixed). I used to do the Milk/Cereal combo all the time with the kids but after Get To Work came out and added illnesses, I've switched to the Juice/Cereal combo.