What should Linux/Unix 'make install' consist of?

I've written a C++ program (command line, portable code) and I'm trying to release a Linux version at the same time as the Windows version. I've written a makefile as follows:

ayane: *.cpp *.h
    g++ -Wno-write-strings -oayane *.cpp

Straightforward enough so far; but I'm given to understand it's customary to have a second step, make install. So when I put the install: target in the makefile... what command should be associated with it? (If possible I'd prefer it to work on all Unix systems as well as Linux.)