A 7812 positive 3-terminal regulator is used for the main regulation, and this is followed by as many power emitter followers as needed for the current you require.
The transistors are not critical. I used 2N3771 devices 50V, 20A, 200Wsimply because I had a whole bunch of them in my junk-box. These are pretty much ideal, but I suggest that you use whatever you can get cheaply. If you use 2N3055s expect to use four transistors for the first 10A, and one transistor for each additional 5A peak or 4A continious output capability to ensure an adequate safety margin.
The LEDs are optional, but recommended. 2.2k series resistors (as shown) will give a LED current of about 10mA, which is pretty much ideal.
The supply is designed to provide very high current, and I used a 300VA toroidal transformer and two bridge rectifiers, one for each winding. The 40,000uF electrolytic is one I had to hand, and provides excellent performance. You can get away with quite a bit less capacitance for the 10A version, but (as always), hum may become a problem if there is insufficient capacitance. The circuit shown will have a ripple voltage of about 4V at 20A load, and this is quite acceptable as the regulator IC will remove the vast majority of this ripple voltage. I was unable to measure any output ripple on my unit at continuous currents up to 10A, although there must be some - it was just too far below the noise voltage to measure.