How do I paint furniture the right way?

Try chalk paint. You don't have to prime first. Youtube has dozens of chalk paint techniques and ideas. Here's a picture of an old buffet that I chalk-painted. Other than making sure everything was clean, I didn't do any priming, even around the bottom where the wood was new. (All the bottom panels had rotted.) This is Paris Grey with dark and light wax.

You really should.

the prepping even before priming is the key. The shinier the finish the more prep. needed. Sanding and filling scratches then priming then painting then sealing. Especially if you want a lasting finish/job well done. Even with chalk paint.

Primer will make the final color more true and vibrant.

I like this tutorial for painting upholstery. She doesn't prime it, but she does mix the paint with a fabric medium. And she shows the chair five years later. It still looks good!

https://www.11magnolialane.com/tutorial-how-to-paint-upholstery-fabric-and-completely-transform-a-chair/