AC to DC wall adapter circuit
They're nearly all SMPS (switched mode power supply) nowadays. Advantage is efficiency, weight and cost - not necessarily in that order. 

12 V is a standard voltage for many computer peripherals - some monitors, routers, etc. - so you should find a surplus one easily. SMPS building is not for the beginner as debugging is dangerous as the switching circuits are at mains potential.

Another alternative is the wide variety of SMPS modules readily available from all the major suppliers.



Figure 1. SMPS block layout. Source: Wikipedia Switched mode power supply.

If you are interested in learning how they operate I suggest that you open some up (with power off, of course), try and find the switcher chip, get its part number and search for the datasheet. Very often you will find that the SMPS manufacturer has used the application note design with small modifications rather than risk designing from scratch. SMPS board layouts can be important as high frequencies are involved and if the manufacturer has a suggested layout this too will be adopted.

Remember the high voltage capacitors will be charged to \$ \sqrt {2} V_{MAINS} \$ and will take some time to discharge.