How does shifting a signal in the time domain affect its frequency domain?
According to the Fourier's transform properties, the Fourier's transform of $f(t+dt)$ would be $F(f)e(j2\pi fdt)$
So, basically, the spectrum (Fourier's transform magnitude, representing the frequency content of your signal) does not change. However, f Fourier's now has a phase-shift proportional to the frequency.

To answer your question : the phase-shift's sign is the time delay's sign.