This question is an exact duplicate of:
If you do not want to use a breadboard, you could solder the wires together of tie them together, so long as none of the wires which aren't supposed to be touching are touching. Or you can also use flex tape! (Don't mind my meme)
A diagram of the internal wiring of a breadboard is found at http://www.fiz-ix.com/2016/04/breadboard-wiring-diagram/
Image duplicated here:
All you need to do is make sure all the same connected points from your breadboard circuit remain connected in the same way on a perfboard or PCB.
There are several ways to make a circuit on perfboard, and this answer on electronics SE shows some examples of using solder bridges as interconnects, short uninsulated wires, and insulated "wire wrap" wires.
You can also find perfboards with the same connection layout as a breadboard for easy transfer from a breadboard-wired circuit, as shown below: