Mix your colors on a pallet, or if you are mixing a larger amount use a container with a lid. Use a cheap brush for mixing. For your first assignment d palette is fine. Always add some water to your paints, but use water sparingly. The consistency of the paint should be like thick melted ice cream.
Dark colors require a lot of white to get to a light color, so start mixing from lighter to dark.
Begin by adding a small amount of black paint on you palette to a larger amount of White paint. For each darker gray continue adding small amounts of black into the Whites moving toward the a near black range at the end. Note that's some areas will appear to look the same even though more black was added to the mixture. This is because at a certain point the amount added to the mixture must increase in order to effect a visual change. Use a small brush to paint the edge of shapes.