The normal way is to use a mains transformer to reduce the voltage down to a suitable level to regulate down to the required voltage. This means you'll need to solder the mains connections to the primary side of the transformer.
If you don't want to solder the nasty mains connections to the primary of the transformer then you'll need a fully enclosed transformer.
Do the two outputs need to be isolated from on another?
If so you'll need a transformer with a twin secondary.
Do you plan to be able to draw 1.5A from each supply simultaneously?
As a general rule the RMS AC input current to the rectifier is the output multiplied by √2.
1.5×√2 =2.2A
Each secondary needs to be rated to 2.2×20 = 44VA, the nearest standard rating is 50VA.
This means if you want to be able to draw 1.5A from each output, the transformer will need to be rated for 100VA.
The trouble is I doubt you'll be able to find a fully enclosed transformer with twin 20V secondariness.
**broken link removed**
LM317 / LM338 / LM350 Voltage and Current Regulator Calculators
For 20V use any of the following combinations for R1 and R2:
R1 = 62R, R2 = 1k
R1 = 130R, R2 = 2k2
R1 = 160R, R2 = 2k5
The filter capacitor needs to be at least 4700µF and be rated for 35V.
The regulators will also need to go on a good heatsink.