Here are Tek-Lok pics that will hopefully explain some of how it works.
First up is a picture of a Tek-Lok mounted on an Okuden sheath. How the holes/eyelets on a sheath are arranged dictate whether or not the Tek-Lok will mount on the sheath and how many mounting variations can be accomplished. Okuden sheaths are designed with the Tek-Lok in mind, so they allow lots of mounting flexibility.
In the picture, the hinge of the Tek-Lok is at the left (toward the bottom of the sheath). Most folks mount the Tek-Lok in the opposite orientation (i.e. with the hinge at the top and the Tek-Lok opening facing the bottom of the sheath, thus approximating the "belt loop" hooks used on non-Tek-Lok sheaths). Putting the Tek-Lok opening down (toward the tip of the sheath) makes mounting the sheath with the knife inserted awkward. The handle, being tilted inward toward your body, tends to poke you in the midriff. I did this too, until Brian Wagner (Mr Okuden) told me to put the Tek-Lok opening toward the top (mouth) of the sheath. If you mount the Tek-Lok as shown in the pictures, the midriff poking doesn't happen. (Unless you've got serious overhang at the belt line.

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Here's a pic of the Tek-Lok profile as it is mounted on the sheath. Note the rubber spacer washers between the sheath body and the Tek-Lok. Besides holding the Tek-Lok away from the sheath body, those washers snub against the Chicago screw posts to hold them in place as you tighten the screws.
Here is the other side of the sheath, showing the mounting screws that pass through the rubber washers and hold the Tek-Lok on the sheath.
To open the Tek-Lok squeeze the flexible prong "ears" in the direction of the arrows, then swing the rotable piece up away from the base.
Flexible prongs pinched in ....
.... and the latch partially opened.
Below is a picture of the latch fully opened. By mounting the Tek-Lok via various combinations of the screw holes, you can mount it left/right, horizontal/vertical, 45-degree cant to left/right, upside down, etc.
Note the bar with the screwhole in the middle of it on the left-side piece. That bar can be slid up and down in the slot (then tightened with the screw) to adjust the Tek-Lok for different width belts.