the link i posted was just first circuit that i spoted. it is a classic power supply with voltage regulator and current limit:
1. transformer steps down voltage and provides isolation from mains. if your mains is 120VAC then that is what primary of the transformer need to be rated for.
2. D1 is single phase bridge rectifier. it converts AC into pulsing DC.
3. C1 is used as filter to smooth those pulses into fairly stable DC (although not regulated)
4. R1 is used to discharge C1 when power supply is turned off
5. D2 and C2 are again rectifier and filter (can be removed, it would be better to have C2 in parallel with zener)
6. R2 and D3 form simple voltage reference (D3 is zener diode). for this to be stable, only small current (mA) is allowed through zener diode (nearly constant current).
7. VR1 and VR2 form voltage divider so one can dial down the reference voltage
8. T2 and T3 are voltage follower, they allow output current to be large while D3 current can remain small. note that this is open loop voltage regulator.
9. R3, VR3 and T3 form current limiting circuit. when output current is large enough so voltage drop across R3 and VR3 reaches Vbe of T3 (about 0.7V), T3 will turn on and Vref will be pulled down (T1 and T2 will follow and output voltage drops). this is how current control acts. unfortunately, sensing voltage is Vbe of the T3 (depending on application, 0.7V may be fairly large). the point is that even if power supply is operating in normal condition (not current limited) output voltage varies with current drawn (output is lower when current is largest). this could have been completely eliminated either by adding feedback to voltage regulator or by moving current sensing circuitry elsewhere (for example in place of D2, it would require more changes).
as others have mentioned, you can use LM317T as simpler regulator and you can also use another LM317T as current limit. note that tihs will make lower limit about 1.2V and not zero (it is possible to get to zero too, but requires additional components). building power supply is good exercise for students learning electronics but since prices of off the shelf products are so attractive (use eBay if store prices are not low enough) it makes little sense to mess with DIY.