HTML 5
Flash is all but dead. There were very good reasons Steve Jobs banned Flash from iOS devices. Those are the very same reasons I don't even have Flash on my computers, and haven't for years. It hasn't been an issue for years. I can't recall the last time a web site required Flash.
*****Oh, wait, yes I can. There are certain government sites that still require it. One day they'll join the 21st century. Maybe. ********
As to what YOU need to do/acquire/install to do without Flash, well, you'll need an OS newer than Windows XP, or Mac X 10.5. You'll also need a browser less than 6 or 7 years from it's last update. Other than that, nothing I can think of.