The full circumstances aren't yet revealed. The bullet points from Secret History...
- We know Kelsier was preserved after dying, and lost his main opportunity to move on at that point.
- We know that without a "tie to the Physical Realm", he's stuck as he is, a ghost, or a shade wandering the Cognitive, depending on how technical you want to talk.
- We know he tried to interfere with events in the original Mistborn trilogy, to limited success, but he did learn he could communicate with people pierced by Hemalurgy.
- We know he made contact with Spook.
Tying that to the Wax and Wayne series...
- We know Spook did an awful lot of research into Hemalurgy, which is kind of odd seeing as it had no apparent end goal besides posterity, or how to use it for "good".
And then with a very large gap of indetermite time in between we have in Bands of Mourning...
- Kelsier is seemingly back in the Physical Realm, long enough to leave a coin imprinted with his own memory behind, inspire the Southern civilization to survive their hostile terraforming, somehow conceive create or discover the Bands of Mourning and hide them, and for myth icons to be crafted depicting him with a Hemalurgic spike in one eye alongside his church's spear iconography (most of which is treated vaguely enough to be mistaken for the Lord Ruler, who is logically powerful enough to do such things, but not the kind of person to do so, and is confirmed in Secret History to not be a candidate).
The most natural conclusion to draw between these items is that Spook's hemalurgy research allowed Kelsier a method to reconnect with the Physical and walk the world once again. How would be a wonderful question. It's not like his distinctive scar pattern would suddenly appear if he was borrowing a body. Did Spook somehow spike his spirit, and poof there he was? Was his original body recovered, is he piggybacking with a Kandra, or something else altogether? Big unknowns, and questions best left for future works, especially since all we have for proof is a word and some scars, and Kelsier has pulled very similar cons before (see OreSeur).
As it is, even this tentative answer - that Kelsier can take physical form with that one spike that Spook made for him - is rife with speculation. We think we know many things. Most of these 'facts' came from Bands of Mourning, which was filled with major misdirections. So take it all with a heap of salt.