The Moon today is in a Waxing Crescent Phase. A Waxing Crescent is the first Phase after the New Moon and is a great time to see the features of the moon’s surface. During this phase the Moon can be seen in the wester sky after the sun dips below the horizon at sunset. The moon is close to the sun in the sky and mostly dark except for the right edge of the moon which becomes brighter as the days get closer to the next phase which is a First Quarter with a 50% illumination.
You can use this link to go forward or backward in time for Moon phase information. If
you are curious you can even find out what phase the Moon was in when you or
anyone else, you know was on the date the person was born