How does a LSF level-shifter work?
The LSF drivers SEEM the most flexible.
These SEEM to be what you want BUT DO satisfy yourself of this. 
Cost of devices from all 3 families are very similar.

You do need to comply with their pullup requirements - too low a pullup value and the weak drive outputs cannot change state.

The TXB family works only with push-pull devices.

The TXS family works with pushpull or open-drain/pullup systems but is less flexible than the LSF family.



Also consider the level translator discussed here 
Depending on yourr speed requirememnts it may suit and it may give you more control over functionality. Or not :-).   

Also see this and all these may be useful. 



Here is an LSF block diagram from fig 2 in the TI Application Report that you cited.
I'll explain a left to right signal transfer and leave you to go from there.

The two FETs are provided to implement a switch that operates when the levels are AT a desired voltage, unaffected by Vgsth = FET gate threshold voltages.  

VrefB is > Vrefa - typically at least 1 V higher (spec sheet says).  

Example:
A-side = Vin.
B-side = Vout.  

VrefB pulls up Qh drain &amp; (connected) gate via 200k.
As Qh turns on stabolises when Qhd / Qhg is Vgsgth_Q2 above Qhs = Vrefa.
ie gate voltage is at critical turn on voltage of FET when FET s is at Vrefa.
BUT Qhg is connected to Qlg so Ql also "just" turns on when Qls is at Vrefa.
So Ql is thus biased to turn OFF when input rises to or above Vrefa and to turn on when Vin falls below Vrefa.
SO - 

Vin high:
When Vin A side is at Vrefa FET Ql is off and Q1d= B out is disconnected from Vin and so Vout is pulled up by VBPU to 3V3.

Vin low
When Vin is puilled low to ground, Ql is on (as QLs below Vrefa) so Ql is on so Vout is pulled low (to ground) so Vout is low when Vin is low.



The LSF series allows different translation voltages on the B side channels by using different pullup voltages on the B side lines.