One more important point before you get started: the TI TPS7A4901 (data sheet) chip used for both regulators is a low noise regulator. This can come in very handy when powering precision crystal oscillators where you want to keep the noise down to maintain short term accuracy. It is not the lowest possible noise. But it is quite good for a one chip solution.
The design files (schematic, board layout, and parts list) for the board can be found at Power Supply Digital WW - design files. If you want to build one OSH Park has the boards for $11.00 each.
So lets start the build. First put the 22uF 6.3 V capacitors (C9 and C10) on the board. Then solder the U1 and U2 pins to the top side of the board. Next turn the board over and squirt some Chip Quick SMD291NL flux into the U1 and U2 grounding/heat sink holes on the back side of the board and apply your iron and solder to those holes (I use 63/37 tin/lead) until they are filled. That grounds the chips and also acts as a heat sink for them.
Now solder the rest of the surface mount components to the board. At this point I like to test the board because trying to work on the regulator chips with all the other components mounted is very difficult (read impossible) without removing parts. To do that testing you have to short out RV1 and RV2 and apply power to the chips. About 6 volts is OK for both chips because no significant power will be drawn - this is only a voltage test. The voltages should read about 2.9 volts for U1 and 4.9 volts for U2. If you don't get those voltages check U1 and U2 (the most likely culprits) for shorted or open pins. Since I plan to make a lot of these boards I built a pogo pin rig for this test using a bare board. The holes for the pins that go into RV1 and RV2 positions need to be drilled out (.040" - #60 drill) if you are using the Mill Max 0856-0-15-20-82-14-11-0 pogo pins to make your temporary connections. It will look like this with the board mounted on the test jig:
Next mount all the 470uF 10 volt capacitors (C3 through C8). Now add in the transistors with thermal pads mounted loosely to the heat sinks. I used 6-32 by 3/8" screws and split lock washers to insure contact of the transistor with the heat sink is solid. Mount and solder Q1 first and then tighten the screw. Then Q2 followed by Q3.
Mount all the rest of the components and test the board under power. I used a 22 ohm 1% 3 watt resistor mounted on a power plug for the 3.3V section and a 33 ohm 1% 3 watt resistor mounted on the same power plug for the 5 V section. Anytime you want to test a supply under load just plug in the load. And that is all there is to it.
I wrote some more about low noise power at ECN Magazine.
Engineering is the art of making what you want from what you can get at a profit.