Newton's universal law of gravitation is straightforward. However, you need to review two things: (1) Newton's third law and its applications (Section 10.2 of Volume 1); (2) Addition of vectors. To get the gravitational field from two or more masses, be sure to compute the (vector) gravitational field at the test point for each mass and then add these together vectorially, i. e., add together the x, y, and z components of the field from each mass. Remember that r in the universal law of gravitation is the distance from the mass to the test point, so when the mass isn't at the origin, you have to first compute this quantity as the magnitude of the vector difference between the position of the test point and the position of the mass.
Gauss's law is generally used to compute the gravitational field for distributions of mass. Applications of Gauss's law always have two components: (1) Compute (or find an equation for) the flux in terms of the field passing through some closed Gaussian surface; (2) equate this flux to -4 pi G M, where M is the amount of mass inside the surface. Gauss's law is only useful when the relationship between the flux and the field is simple, i. e., the flux = field*area. This simplicity only exists when (1) a high degree of symmetry exists in in mass distribution, and (2) the Gaussian surface is defined so as to take advantage of this symmetry, i. e., a sphere for spherical symmetry, a cylinder for axial symmetry, etc. Gauss's law is always true, but it is generally only useful when such symmetry exists. Sometimes an apparently complex mass distribution can be reduced to a sum of a few simple mass distributions. Use Gauss's law separately to get the gravitational field for each simple distribution and then add the fields vectorially to get the total field.
You should know where Kepler's laws come from, at least in the special cases that we considered. Review Chapter 11 on rotational dynamics.
The trick in using conservation laws is to realize which are applicable to a particular situation. For planets and comets moving in Keplerian orbits, conservation of energy and angular momentum hold. Conservation of linear momentum is inapplicable because an individual planet isn't isolated, so its linear momentum is not conserved.