All antibiotics, including penicillin, start to work as soon as they enter the bloodstream and arrive at the infected site. (Obviously an injection of penicillin will start to take effect quicker than an oral dose which has to enter the bloodstream though the digestive tract).
The reason that the effects aren't usually felt very swiftly is that, in most cases, it's not the bacteria which actually make you ill. It's the toxins which they produce. Even though the antibiotics are attacking the bacteria, the toxins remain in your system until the body can remove them.
For most types of minor infection, the majority of people will start to feel better a day or two after the treatment starts but, in some cases, it might take several more days.
Chris