It’s possible to find Vault Key Fragments on your own–i.e. perhaps you luckily stumbled upon one of them while exploring. But if you tagged an Order Silo, then you should see a glowing radius on the world map. The Vault Key Fragment is somewhere within that area.

If you head to that location, a bar will appear at the right-hand side of your screen. The yellow pips on the bar will keep increasing as you get closer to the item.

Note: Let’s say you’ve already obtained the three Vault Keys in a region. If you check the world map, a larger circle should show the general location of the Vault’s entrance. The process remains similar, so just make your way to that area and see if the bar gains more pips.