How do I add grounding to my old electrical wiring?
The rules on retrofitting grounds were greatly relaxed with the 2014 electrical code (NEC 2014). Yes, now you can simply run bare or green wire between all your electrical boxes and back to the panel.  

The ground wires can follow any feasible route, they don't need to travel with the conductors.  

The ground wire must go back to the same panel as the conductors come out of (that's relevant if you have more than one panel). 

The ground wires MUST be thick enough (generally as thick as the conductors) and can be thicker -- for instance a 12 AWG ground wire is not acceptable for a 10 AWG/30A dryer circuit, but it is acceptable for a 14 AWG/15A outlet circuit. 

Here's the whopper: Multiple circuits can share grounds. You don't have to home-run the ground all the way back to the panel, you need only reach another grounded point whose pathway is thick enough.  So you can daisy-chain your grounds from box to box, as long as all the circuits you are grounding come out of the same panel.  Or, your 10 or 6 AWG ground to your range or dryer can be a "backbone" providing grounds to many other receptacles. 

All ground splices must be done with the same rules as any other splices: inside a junction box or using some sort of splice listed for use outside of a box. 

For details,  see the National Electric Code, NFPA 70 (2014) Article 250 — Grounding and Bonding.  (NFPA now offers free access online to its codes and standards.)