On my Samsung Galaxy HomeScreen, it used to be easy, go to Chrome, visit that url, go to settings, choose "add to home screen". But now, it seems that some sites have their own "app" version, such that the phone would detect this and replace "add to home screen" to "install app" instead. I had since copy pasted a list of my NJTransit links (for different stations) to a notepad on my phone and click the links from there, not the most satisfying, but I tolerated it for a long time. I tried setting the site to "desktop mode", still no help.
Now, thanks to some site, the trick to the solution is just to go offline (airplane mode) before going to the sites. This way the browser wouldn't be able to detect if these sites are app or not, and allow the default option "add to home screen".