Review the structure and reactions of esters and phosphates (actually, phosphate esters), especially hydrolysis of these compounds. Also review the synthesis of esters from carboxylic acids and alcohols, and the synthesis of phosphates from phosphoric acid and alcohols.
A key to understanding the bewildering array of complex lipid structures is to start seeing them as simpler substances (fatty acids, glyerol, phosphate, and alcohols), joined by familiar functional groups (ester, phosphate ester, or amide). One way to develop this insight is to memorize how to put complex lipids together from their components.
Find a table of fatty-acid structures and memorize the structures of palmitate and oleate, examples of some of the most plentiful saturated and unsaturated fatty acids, respectively. If you don't already know it, learn the structure of glycerol. Take another hard look at phosphate ion.
Now look for a table of glycerophospholipids. Learn how to draw phosphatidate, the parent compound of glycerophospholipids, starting from structural formulas of any two fatty acids, glycerol, and phosphate. Then look closely at how the "head-group substituents" (alcohols) listed in the table are joined to phosphatidic acid to make a glycerophospholipid. CAUTION: Several of these alcohols (serine, for example) could in principle be joined to phosphatidic in more than one way, but only one way corresponds to the naturally occurring structure. So look carefully at the linkages, and draw out some full glycerophospholipid structures. Your learning goal is to be able to take the structures of the components and correctly link them into a drawing of a glycerphospholipid (see quiz below).
Now look for the structure of a sphingomyelin. Study it in the same manner, until you can draw a typical sphingolipid if you are provided with sphingosine, a fatty acid, phosphate, and an alcohol. Note that the fatty acid in a sphingolipid links to sphingosine by an amide linkage instead of an ester linkage, and note also that one of the nonpolar tails of a sphingolipid is part of the spingosine molecule itself, rather than being derived from a fatty acid.
With this little memory task under your belt, you'll find it much easier to read about the variety of lipids that make up fats, oils, and membranes.
(At first class on this topic)
Instructor will provide drawings of fatty acids, glycerol, phosphate, a common "head-group" alcohol, and perhaps sphingosine. Instructor will ask you to assemble them into a structural formula of a glycerphospholipid or sphingolipid. You don't need to recall any of the component structures in order to carry out this quiz; you simply need to know exactly how the components are linked together.