Ever want to see a Great White Shark up close? If so, this is a once-in-a-lifetime opportunity to go out on a boat, step into a cage attached to the boat, and watch the sharks casually swim by. Keep in mind that the water is freezing, even with the thin wetsuits provided by the boat operators.
Although this adventure usually takes place in Gaansbai (due to the higher percentage of Great Whites in the water there), you typically will be picked up in Cape Town at a hotel or hostel by the tour operator (usually very, very early in the morning). Unfortunately, it's pretty rare to just show up in Gaansbai and jump on a shark diving boat. Instead, you'll need to book with a legit tour operator.
One of the more eco-friendly and nice operators is Detour Africa and they offer full day shark diving trips for a little less that $100 USD (R1195) that includes a shuttle pickup from your hotel/hostel, a breakfast, unlimited snacks while on the boat, wetsuit and snorkel gear, a lunch (with free wine), and a ride back to where they picked you up from.
After booking with a respected tour agency for no more than $100 USD, simply follow their instructions as to where to be picked up at and get ready for a day of adventure.
It's reasonably safe, so long as you don't jump overboard and the tour operators usually give a lengthy safety briefing beforehand. If you want to see what it's like, check out this video I made a few years ago.