Certifications and requirements
The more I learn about regulatory compliance, the more I'm convinced that I don't know anything.  This is a giant maze of international laws that is difficult to navigate.  What I wrote below is just a rough guide, to be taken with a grain of salt.  But my last paragraph is very important:  You need professional help (not mental help, that I know of anyway).

There are a variety of regulatory standards that you must adhere to.  Most of them are going to center around EMI, Electrical Safety, and Materials Safety. 

EMI, or Electro-Magnetic-Interference, is concerned with what interference your box is spitting out and receiving either through the air or through the AC power cable.  Spitting out would be EMI Emissions, and receiving would be EMI Susceptibility.  Emissions is how your box effects other boxes, and susceptibility is more like will your box work when someone is on their cell phone near by.  A somewhat related aspect of this is your boxes tolerance to static electricity zaps.  In the USA, this falls under the domain of FCC compliance testing.  In the EU, it's part of the "CE" approval process.

Electrical Safety is concerned with things like:  will your box burst into flames or electrocute the user.  In the USA, this is normally certified by an independent lab, like UL or TUV-- I'm not sure about other countries.

Materials Safety is mostly about the use of lead, but does involve a whole list of bad things.  In the USA, I'm not even sure there is anyone who cares what's in the device (as long as it isn't medical or food related).  In other countries it's referred to as RoHS or other names, but I'm not sure if that falls under "CE approval" or not.

The important thing to know is this:  In the practical sense, you cannot self-certify.  Doing this compliance testing involves lots of expensive equipment and knowledge and it's simply not practical to do it yourself.  Fortunately, there are companies that specialize in this.  

Find such a company, and use their expertise to not only perform the tests, but to give you solid information on the whole regulatory compliance testing/reporting process.  In many cases these companies will also file all the paperwork with the various government groups, etc.  These companies are often well versed in not only your countries regulations, but also international regulations.  I'll warn you that this process is not cheap, and not fast.  But that's the cost of doing business.