How can I run the current file in PyCharm

As it turns out, the action I was seeking is "Run context configuration" (or "Debug context configuration" for debugging). The default key binding on Windows is ctrl+shift+f10, or ctrl+option+R on Mac, as Ev. Kounis pointed out, although you can bind it to any key you like.

These settings can be found under the "Other" section in File->Settings->Keymap. The easiest way to find them is to simply use the search box.

Just right click on the tab of your file and click run "file name" or you can press CTRL+shift+F10

The key combination you are looking for is Ctrl + Shift + F10. This will run the current script with current being the one displayed in the viewer.