References to draw 3D molecules with directionality of non-bonding electron pairs and p-orbitals
As it is already pointed out in the comments, what you are learning for is hybridisation and some basic MO theory. Do not go too far into the MO direction, because you will get into somewhere completely different place, and you will hard time to make the connections. 

So aftre you reviewed hybridization: Once you can identify in a molecule the sp1, sp2 and sp3 carbons, you should be able to orient the hybrid orbitals. For example in the case of sp2 carbon of the lower image, it is in the HHCC plane. In case of sp1 there are two, for sp2 one un-hybridized p orbitals. These unhybridized orbitals should be perpendicular to the hybridized ones: perpendicular to the axis of sp1 or the plane of sp2.