Small PSU with 110-240 Vac 50-60 Hz input and 12 V @ 1 A output
For universal input (generally 100 V to 240 V, 50 - 60 Hz) you will use a switched mode power supply. The switched mode regulation circuitry will maintain stable output voltage. Efficiency should be &gt; 85%.

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.
SMPS power supplies are not for beginners as any debugging would have to be done on live circuits with DC voltages of \$ \sqrt 2\$ times mains voltage. Remember the high voltage capacitors will take some time to discharge.
Adding a linear regulator is a poor design decision. It generates heat and reduces efficiency.