How do you use them?

Oh, you mean an F-LINK. Here's me, wondering what a "Lonk" was...
F-links are pretty straightforward; they're basically short-range teleporters that warp you to the point where you first used them. It's like a "Mark" and "Recall" spell built into one object, if you understand that metaphor.
1. Select it from your backpack to equip it.
2. Hit the "use object" button to activate it, just like you would with a weapon. It'll drop a small yellow diamond-shaped object on the ground. Do not pick this object up, or you'll have to start over.
3. "Use" the same F-link again at any time to instantly be returned to the diamond's location. Note that using the F-Link causes you to automatically pick the diamond up, so you have to set it up again if you want to teleport to the same point another time.
I'm not sure if the F-Link can be used to transport you from region to region, but within regions you can use it to get quickly from place to place.

Yes, my bad! A typo. :)

F-Links do not work between regions, only within the same region. Also note that if you have F-Links "deployed" in a region and travel through a Daoka, the F-Links won't automatically be collected; so if you want to get them back, you'll have to travel back to the region to collect them.

I know how to drop the arrival platform but after I drop one it simply vanishes from my backpack. I don't see how to active it again to return to the platform.

There are three F-Links in my back back
1) one with a blank sqaure
2) one with a square with lines inside and an arrow pointing up, under the square
3) one with a square with lines inside and an arrow pointing sideways, to the left of the square
I've tried a number of combos for the depart and arrival schemes but all that seems to happen is that the F-links simply fall to the ground. Can someone provide a more detailed explanation?

After you use, say, the square f-link, and drop it to the ground, you'll have a NEW f-link item with a square in your inventory that warps you there. It doesn't appear in the same spot in the inventory as the f-links before they are activated. The thing that falls to the ground is the destination, step away from it and find the same shape device that is now in your inventory and use it to warp to the destination.

That's right, i did search this new one for a long time too. It was located in the first 2-3 rows of the inventory. But don't choose the PPS by mistake, it looks really similiar ;)

BTW:
im very interested in one question. Is this item called F-Link in all languages? I am asking, because in Germany "flink" means "agile, alert", and i can't imagine Infogrames / Appeal did think on this meaning by naming the item.

To be fair, f-link is a little different than flink. This brings up another point - what is the F supposed to stand for? I find most of the terminology in this game to be quite amusing.

All hail the Yods!