Much of the regulation comes from the EU and is standardised. The main areas that may apply are:
EMC certification against the EMC Directive. This may involve testing for unintended emissions and susceptibility to induced (via power cables, for example) or radiated (from nearby transmitting devices) interference that prevents the device from functioning as intended. Generally the latter part may not apply if the device is fail-safe, in that no hazard would be caused if it was susceptible to interference.
Approval to the Low Voltage Directive applies to any device that operates at, or has voltages in it, that exceed 75V DC or 50V AC. Most battery powered Picaxe projects would be exempt from this, but if used with rechargeable batteries then the charger needs to be approved.
Compliance with the ROHS requirements, which means ensuring that there are no hazardous materials above a certain limit within the product. The most obvious being lead in solder, hence the insistence on the use of lead-free solder, but there are other materials to look out for in components, particularly things like cadmium and beryllium.
If you want to have the product CE marked in order to show that it is compliant with the EU regs, then this has to be approved by a Notified Body. You can self-certify in some areas, but you don't have the authority to use the CE mark without the approval and registration of the product with a Notified Body. In order to get this approval you will need a form of quality assurance that provides as a minimum traceability and certificates of conformity for all materials used, and may be subject to audit to make sure records are being kept.
There is a way around this that I have used for hobby projects (and I used to be Head of Type Approval for all UK marine radio, radar, safety equipment and nav aids, and a Notified Body) and that is to sell kits of parts. Because you're not selling a product, as such, you are not required to show that what your selling complies with any regulations, you just need to be comfortable that nothing your doing creates a liability that you may be unwilling to accept.
In my case I produced kits for a simple electronic capacitive fuel gauge for use with paramotors. This was battery powered, and I sold a circuit board, instructions and all of the components as a kit, with instructions as to how they might be put together. Because the fuel tanks of each paramotor were slightly different, I left it up to the kit builder as to how they wished to make and install the probe, and only supplied some lengths of concentric brass pipe in the kit that could be used to make a safe probe. I stressed that it was up to the builder to make sure this probe was safely constructed and fitted to the fuel tank, but did use a special chip for the sensor that was certified as safe for direct connection to such a probe. It was perfectly legal to sell these as kits and I did not require any form of certification or approval. Most who bought them had never used a soldering iron before, so I did offer a service where I would check any board post-construction, which in reality meant re-making a lot of solder joints much of the time.