When you published your software in a journal that accepts submissions that are primarily about the software, you could try to use the citation databases to retrieve citations or view counts.
Other indicators for research software are the ones supplied by the repositories themselves. GitHub uses for example: Followers, Forks, Watchers, Collaborators, Gist Count, and Downloads. SourceForge, next to downloads, only adds an average rating of the software users as an indicator. Other software registries might even use different indicators, but the general problem is that these usage data are anonymized hindering a further analysis of who, why and if the software is used.
An exception and promising tool is the Dutch Research Software Directory, although not used much (yet) by UM researchers. This tool lists under Mentions the sources where the mentions stems from, and with the links to the online sources one can assess who and why they are mentioning (or using) the software.
To assess the FAIRness of our research software check: https://fair-software.nl/
To make the research software easy to cite, besides assigning a DOI to the software version/release, you should provide a CITATION file as part of the documentation of the software. This can be a human readable file like a plain text file (e.g. as part of a ReadMe file) in the root directory of the software with information about how to cite the software. Or, it can be a machine readable file like in this example. The tool CFFINIT allows to easily create software citation metadata files.
the Dutch Research Software Directory.
A non-exhaustive list of journals accepting software submission