By cables from the case do you mean the jumper cables for the power button, and maybe a couple SATA or USB 3.0 cables?
As for the PSU, if you have a modular one only plug in cables as you need it. The absolute ones you need are the CPU cable, either a 4 pin or 8 pin connector, PCI E ones for your GPU, either a single 6 or 6+2 pin, or 2 6+2 pins and lastly a 20+4 pin that goes to the mobo.
NOTE: Try to route every PSU cable to the back side of the mobo through the cable management slots or into the HDD cage depending on what works best first and then have them go to the proper part. Keeps your case clean.
The best way to route the CPU cord is to run it along the back of case under the GPU, or use the cable management of your case and see if you can route it around the backside and up and over. my cord was too short to do this.
The rest just route through the back side then get them to the proper component.
Post your system specs please.