How can I get the version of SharePoint that is installed on my server?
If it's up and working, or just a webserver running SharePoint and you don't have access to console/admin/registry or s.th. else, just good ol' browser, you might add _vti_pvt/service.cnf after your base SharePoint-URL to determine the version number.
You'll get something like this:
vti_encoding:SR|utf8-xx
vti_extenderversion:SR|15.x.x.x
And Versionmapping... As far as I remember (please correct me if incorrect):
v12.x = SP2007/WSS
v14.x = SP2010
v15.x and higher = SP2013
Dunno the one for SP2007 anymore.
Just had to figure this out and found this answer is missing here, though you might (?) not be able to get more insight, just the general version (as said, please correct me if it's more specific, in the comments).
Edit: Here you can find the exact Version numbers from SP2007 to SP2013: http://blog.fpweb.net/what-sharepoint-version-am-i-using/#.VBlbNucv-9Y (you have to scroll a bit, just under the mid of the article).