Nothing has changed in the methods of selecting, you're using exactly the same software (OS and App) as you were on the old machine. The difference is in settings for the trackpad, and you might have forgotten some custom changes you made years ago.
I think the one that is trapping you is that a two fingers press on the trackpad is the secondary click, it behaves like right clicking a mouse and pops the context menu. Take a look at the options in > System Settings > Trackpad.
As far as guides goes, there are some clues in Apple's support docs, these two I found easily but there are probably many more if you search Apple Support
Use Multi-Touch gestures on your Mac - Apple Support
MacBook Air trackpad - Apple Support