This doesn’t matter very much, I know. But the small section of the population who does notice moon phases, and/or are astronomy buffs, will appreciate your being accurate about it. So here is the quick-and-dirty guide to how the moon works:
The waxing moon (the phase in which it’s gradually getting more illuminated—“bigger,” we say) begins as a very thin crescent at sunset, just above the sun in the west. Its back, its illuminated edge, will face the sun; the points will point away from the sun.
That’s how it always works, of course: the sun illuminates the moon, so the bright side of the moon is the side facing the sun, and the points of the crescent therefore always point away from the sun.
As the waxing moon gets brighter, it rises a little later each night, so that it’s a bit farther to the east at sunset than it was the previous night. Waxing moon can thus be seen in the afternoon too, before sunset, but not in the morning and not for very long in the night; it sets sometime during the night.
The full moon always rises right at sunset. Sun in the west, full moon in the east, shining at each other from opposite horizons, sun fully illuminating face of moon.
And then we are in waning moon phase. After the full, the moon starts rising after sunset, later and later each night as it becomes less illuminated (“smaller”). Waning moon can thus be seen in the morning too, till it goes fully dark and starts over again. (That's the new moon, which rises and sets with the sun, which is why you can’t see it.)
This page has some good tables and explanations on moonrise and moonset too, written by a proper astronomer.
We have some lovely waxing moon going on right now, by the way!