Citing Nominatim & OSM in scholarly journal?

The approach taken may vary according to the citation policies of specific journals. There is a huge research literature on OpenStreetMap (probably tens of thousands of papers now), and probably the easiest thing is to check through some of that for examples. One type is a very simple "OpenStreetMap. https://www.openstreetmap.org/ (2020)." in Stowell et al. (2020).

Other types of citation:

• General overview: 2 books have been published on OSM, Bennett (2010) & Ramm, Topf & Chilton (2011)
• Multi-author books: classic example would be Arsanjani, J. J., Zipf, A., Mooney, P. & Helbich, M. OpenStreetMap in GIScience: experiences, research, and applications. Lecture notes in geoinformation and cartography (Springer, 2015).
• Early research work on OSM: authors such as Haklay, Zipf & Mooney pioneered academic investigation of OSM, and consequently these early papers are influential
• Data. Probably best to cite when accessed and which site (e.g., OSM Planets or Geofabrik downloads.
• Wiki. Include access date
• Software, e.g., Nominatim. Ideally include date used & version

The latter three points will be significant if anyone wishes to replicate reported work.

One last point, if data derived from OSM is a published output this must be licensed appropriately (typically under ODbL).

Did you already have a look at this licence page from OSM foundation?

What point is clear to you, and where do you get stuck in detail?

You want to publish data (and no tile graphics) derived from raw OSM data, or from search results from Nominatim?