How to model pipe intersections?

You can have a look at this course:

https://cgcookie.com/courses/create-realistic-industrial-environments-with-blender-and-eevee

And there are Pipe Joints available, if you enable the  Mesh:Extra Objects Addon and the Loop Tools Addon has a nice Bridge function that can be helpful:

You can also start by Booleaning pipes and then work from there...and there is the Spin Tool...

Well also as you model more and more things, you'll know who to model those pipes intersections, so don't stop at just watching pipes videos. Modeling in general will do.