How can I make connection on pcb (circuit board) holes without solder (for prototyping)?
Solder a pin header
Typically you solder pin headers to these boards. Either male or female. With male pins, you can solder them with the pins pointing down, so you can put them in solderless breadboards.1
1. This may ruin the breadboard strips
Use grabber test clips, which are basically like smaller alligator type clips.
Though regular alligator/crocodile clips may work, depending on the size or how many side by side ones you need. I have some really mini ones.
Yes, the pads should be plated on the inside as well as the top and bottom, electrically connecting them.
No, just pushing a standard 0.1" header into the hole won't work. They are not offset holes, or push fit tight. They are generously loose. Some people have used rubber bands but that's not very secure.
For me I would rather use these PCB terminal blocks, which you can easily remove and connect your wiring without worrying about loose connections every time.