NASA Jet Propulsion Laboratory posted a brief video which highlights some events you ought to try to see this month. The first two are conjunctions of familiar objects in the sky. Neither requires any special equipment. The events in the second half of the NASA video will require at least a small telescope.
Sky & Telescope magazine adds some detail to the conjunction events in this article. The first chart is for the evening gathering of Mars and Venus on the 7th. It will be a similar view for several more evenings. Venus is bright and easy to see. Mars is more difficult. Use binoculars if you have them. Watch as they come closer during the week ahead.
I used my desktop planetarium software to track the movements of Venus and Mars until late February. This video of the screen shows what to watch for each evening.
This chart shows the movement of the Moon for several mornings one hour before sunrise. Saturn and the Moon are near each other on the 12th and 13th. Also watch how the crescent of the Moon narrows from day to day.
A beautiful event involving Jupiter and three of the Galilean moons happened on January 24. Europa, Callisto, and Io were seen passing in front of the giant planet and casting shadows on the cloud tops. Click the image to see that full story at Astronomy Picture of the Day.