If you are running from the source directory, the vim binary is built under src/vim To run vim-Qt you can either call vim with the "-g" argument
$ ./vim -g
or you can create a symlink, or rename the binary, to either gvim or qvim
$ ln -s vim qvim $ ./qvim
Running vim under any of those names should launch the GUI automatically.
If you have issues rendering fonts in vim-Qt try setting the QVIM_DRAW_STRING_SLOW environment variable, e.g. in Unix systems:
$ QVIM_DRAW_STRING_SLOW=1 ./vim -g
or in the windows console
set QVIM_DRAW_STRING_SLOW=1 vim.exe -g
this will be slower, but should resolve most font drawing issues that you have.