You do need to enable VPN if you're off campus, yes, but that's it. It's super simple, you don't need to go though library's website or anything.
I use Google Scholar search exclusively to find papers and you can directly click the link to open the paper (and then download). Constantly copying pasting title, URL or DOI into sci-hub is actually a hassle in this respect when you're just browsing around (I guess there must be extensions or userscripts to make it better, though).