Today I streetpassed someone, who also played Fantasy Life. I went to the streetpass-clerk in the game, and I can see the profile of that other person. I saw that she had a gift, Black Onyx. But how do I get this item? I don't see it in my inventory, nor does the clerk have any option that will give it to me.
First thing to do is to get the player into your town. You do this by going to the StreetPass Clerk in the Guild Office.
Next, you need to find the Mii hanging out around town (not sure if they are found in towns other than the starting one). You can sort-of use the map by looking for blue dots indicating a streetpass Mii's location, but they are not set and will appear in multiple locations.
Talk with the visiting Mii and you will increase your friendship with them.
Leave town and return to re-set the Mii's position and allow you to continue talking with them.
Once your friendship with them is at 100%, they will give you their item.