I don't have experience with SQL Server Spatial, but have enough experience with PostGIS to say that someone giving you data in this format is a big "screw you". If I had data in PostGIS and needed to share it with someone, exporting it to a portable spatial format (like Geopackage or shapefile) would be trivial. Creating a database backup would probably be harder, and frankly, if there were some reason I couldn't export to a spatial format (and I'm having a hard time understanding what that reason could possibly be), I would do them the favor of saying "I can't give you this data" rather than the not-helpfully-helping by delivering a database backup to someone who was unfamiliar with PostGIS (as you are unfamiliar with SQL Server).
The steps to do this involve the following:
- Install SQL Server. This is off-topic, massive, and should be researched indpendently.
- Restore from backup. See for example https://stackoverflow.com/questions/1535914/import-bak-file-to-a-database-in-sql-server.
ogr2ogr to export to your desired output format. See info on the OGR driver for SQL Server Spatial at https://www.gdal.org/drv_mssqlspatial.html.
My recommendation is that you ask again for an export to a spatial format, or, if the data happen to be point data, perhaps a CSV with point coordinates.
If the person is not willing to accommodate this request, you should probably assume the data are unattainable and pursue alternative sources.
If you are not willing to abandon this data, you should research 1 and 2 using official documentation, StackOverflow, and DBA.SE. Once you have SQL Server up and running, an appropriate follow-up question for this site would be "How can I export a spatial layer from SQL Server".