A shapefile is not a single file as commented by Spacedman. You require at least three files i.e.,
.dbf which contains the geometry attributes
.shp which carries the geometry and
.shx the index file.
These files are generally accompanied by a .prj file which carries the projection details.
You can load the vector layer in QGIS and check it's attributes by right-clicking on the layer name in layer panel. If the attributes are present, you can display any one label on canvas by checking display label and selecting the attribute column to show in properties->label option in right-click on layer.
You can also load a .csv file as delimited text layer and choose the coordinates columns or WKT column to load in the canvas.
If the attributes/coordinates are not there and as specified by you the zip file also contained a .csv file which lacks the coordinates. In this situation you can go for table joins options by selecting the No geometry (attribute only table) option while loading the delimited text layer. After loading this .csv it will not show any geometry in the canvas. Now you need to go to the layer properties and select the join operation by linking the shapefile and this .csv file through a common column (similar to primary-foreign key in relation).
A detailed decriptiondescription is given at qgistutorials