The cell membrane is made up of something called the phospholipid bilayer. This is exactly what it sounds like:a hydrophilic phosphate head on the outside and a hydrophobic lipid on the inside.
They form a bilayer as the hydrophilic head faces outwards as it attracts to water, a second phospholipid does so in the other way, meaning there is a phosphate head facing into the cell and out of the cell.
The bilayer is also intermittently filled with proteins, these can be proteins that are on the outside surface, perhaps acting as extracellular receptors, or inside where they act as intracellular receptors, or scaffolding proteins that give the cell shape. You can also get transmembrane proteins that span the whole bilayer, an example of these could be protein channels.
Furthermore there are also glycoproteins and glycolipids that are important in cell recognition.
Cholesterol is also found in the bilayer, this makes it less fluid, but more flexible and strong.
I would also normally support this with a diagram!