What rules govern running mains electricity (220v ac) on a printed circuit board?

Firstly, what are you trying to do? Who will be operating this device? A qualified user? Where is it to be used? What else connects to it? Will this be in a plastic box? Or a metal box? Will there be holes near the PCB? How big? Does it hang on the wall or sit on the desk? These are some of the questions you need to ask yourself.

Your main concern is safety - No fire hazard, no shock hazard, no excessive heat, no mechanical hazards, no radiation, no chemical hazards, etc.

There are several safety standards that govern the construction, such as UL/CSA 60950-1 (http://ulstandardsinfonet.ul.com/scopes/scopes.asp?fn=60950-1.html) for ITE, IEC 60065 for A/V devices, IEC 61010 for Measurement equipment.

One of the main rules is that the PCB needs a minimum flame rating of UL94-V0 (FV-0 in Europe).

Traces if they carry mains, needs to be a minimum width for the current they are intended to carry, so they don't open or melt in case of an overload or short-circuit condition.

The distance between traces (creepage) needs to be considered, based on type of PCB material, the place of installation, and other factors.

How do you determine the minimum creepage? Will now you need to refer to the appropriate standard for the type of product. For example, IEC 60950-1:2005 specifies Table 2N.

How do you determine if your construction is safe? Again you need the standard for guidance.