The person I will be looking for is Francis Plaine Smith. I do not know when he died or where. But, I do know he was living in Oyster Bay, Queens, New York at the time of the 1870 US Census and that he does not appear in any subsequent censuses.
1) First I went to FamilySearch and narrowed the collections down to just New York:
2) The collection I want, "New York, Probate Records, 1629-1071" is at the bottom. I'm going to click on "Browse Images" to the right of the collection title. Once I do, this comes up:
3) A listing of New York counties appears. Since Francis' last known address was in Queens (circled in red above), I'm clicking that one. Then this appears:
4) A listing of everything available for that county comes up and I scroll up and down (note the red arrow) until I reach what I am looking for. Not all counties have a general index of names volume(s), though each individual record volume (i.e. "Letters of Administration, 1864-1868 vol G") seems to have a name index towards the front. In the case of Queens, there is a general index of names and I clicked on the one I believed Francis was in, "General card index 1787-1900 Rhoads, William-Zubrod, Charles." This opens up the volume and I hunt around until I find who I believe to be my Francis P(laine) Smith:
Note the image field box (within the red box). I began my search by typing in a random number in this box, then another until I had narrowed my search down to the image I wanted. The previous image also concerns this same Francis P. Smith:
5) According to the card above, Francis' will can be found in volume 4, page 231.
On image 6, I find:
6) Next, I want to find page 231. Page numbers and image numbers rarely seem to correlate, but I'll type in 231 in the image field box (see screenshot 4 above). It takes me to pages 440 and 441, so I know to halve my next search. I type in various numbers until I reach page 231, which ends up being on image 124:
I am so thankful that FamilySearch added these documents. If you have New York ancestors this collection is certainly worth a look. I hope this makes navigating FamilySearch easier, if not I'd be happy to help.
Disclosure: I am in no way affiliated with FamilySearch or The Church of Jesus Christ of Latter-day Saints, nor did I receive any remuneration of any kind from anyone for writing this post.