Or will people need to download a specific browser?
Hello and welcome @7up !
There is a specific browser. It’s called the SAFE browser. To get more insight into the SAFE network, see here: https://primer.safenetwork.org/
The SAFE-network have a own secure protocol, safe://, to connect with the network nodes. A browser like Chrome or Firefox won’t know what to do with safe://. Similar to Tor that uses a Tor browser. But Safe have a own browser that is not dependent on Firfox as Tor is, to prevent DNS-leaks by not allowing access to the regular http:// protocol.
As @Dimitar wrote, look at the link to the Safe primer for more info.
To add, that doesn’t mean a third party cannot create a browser plugin for chrome, Firefox, etc. The priority is simply to get as secure an experience possible as a baseline. Where it goes after that will be up to the wider community of developers.