Yes, it's quite possible to visit Antarctica as an ordinary person. One of my clients took a trip to the frozen continent back in 2016. Antarctica is mostly open for research workers but that doesn't stop travel groups to offer the Antarctic tour. 

The most common way of visiting Antarctica is through a cruise ship from Ushuaia-Argentina. The total cost of an Antarctic tour can be anywhere from $5K - $20K depending upon your preferences. This depends upon the type of room (on a cruise) you're willing to book and the overall duration of the tour. 

You may not be aware of it, but there's also an airport in Antarctica that mostly consists of a barren icy runway. 

If you're really up for the adventure, make sure to book your tickets at least 9 months before the tour date. For instance, bookings for November 2021 tour started in late 2020 and it will be closed by the end of March 2021. 

Visiting Antarctica has been on my checklist for over a decade - Hope to visit there someday.