Boost converter 3.3 to 5V MAX756
The circuit is a boost switched-mode power supply.  Basically it stores energy in the inductor and the capacitor, switching back and forth with a transistor at high speed according to a clever signal which depends on the output voltage.  (Ask a question about "boost switching regulator" if you want more on this). The basic circuit is like this (which you can see from the block diagram of the datasheet).







simulate this circuit &ndash; Schematic created using CircuitLab

Referring just to the datasheet and the typical application circuit:


From datasheet.


"If the low-battery comparator is not used, connect LBI to VIN and leave LBO open"
Connect /SHUTDN to VIN, "Do not leave the control inputs floating"
FB is 3/5 on the 767, connect to GND for 5V.
Use the other component values they tell you, but pay attention to the notes:


"Best performance is obtained by using specialized low-ESR capacitors,"
Inductor which has extra notes in the datasheet: "For highest efficiency, limit L1’s DC resistance to 0.03&Omega; or less."
"For optimum performance, a switching Schottky diode, such as the 1N5817, is recommended."





After edits to question:

Yes, you definitely need both C1 and C2.