How do I install a "Lite in the Box" (brand) faucet?
This is very standard mixer tap setup. Basically you run the flexible piping through all the holes etc that you need to do to connect it to the main. You do this before you have fixed the mixer in place. Then, you feed the two small ends up through the mounting hole on the kitchen sink and screw them in.

There will be a long bolt with a slot for a flat-headed screwdriver. Make sure that is installed as well (tighten with a screwdriver so it's tight).

Then you put the mixer with the three attachments (the two flexible pipes and the threaded bolt) flush with the basin, and facing in the correct direction.

Then, using a tube spanner (available at any hardware store) you screw in a butterfly fitting and the nut from beneath. This will hold the mixer tight against the bench top. A tube wrench is important because otherwise it's typically impractical to do up the nut tightly, due to limited space and the length of the bolt.