The ultimate answer is that the solar system "is complicated", any answer is subject to challenge and endless qualification and limitations as to scope of relevance and precision. These qualifications often seem pedantic while not being wrong. I will give an answer anyway.
The Earth-Moon binary planet system rotates about its centre of mass (barycentre) with a period of 27.32 days with respect to the stars (sidereal month), however (because the sun is so much further away than the moon) the paths of both the Earth and Moon are always concave towards the Sun. This orbit is only slightly out of round with an eccentricity of 0.0681 (circular would be zero). The plane of this orbit is called "The Ecliptic", and only varies slightly over time (largely due to Jupiter). The Moon's orbit about the Earth is more complicated.
If you actually want to calculate orbits and positions then I refer you to "Astronomical Algorithms" by Jean Meeus, it will introduce you to various techniques including the VSOP series of techniques, for even more advanced and accurate methods you would go for the JPL ephemeris
https://ssd.jpl.nasa.gov/ephem.html these have navigated spacecraft accross the solar system with severe accuracy.
