Look at the molecular structure and formula for ethanol and compare it to the molecular structure and formula of dimethyl ether. Notice how they contain same molecular formula, C2H6O.
Compare the molecular structures. Notice the differences in how the atoms are arranged around each other.
Count how many carbon, hydrogen and oxygen atoms are in each structure to make sure they both come out to be C2H6O. Because they have the same formula but different structures, this will determine that that they are structural isomers of each other.
Look at the two optical isomers of lactic acid. Notice the arrangement of the atoms in the structure.
Notice how the structures are mirror images of each other, with lactic acid (+) having HO on the left and H on the right, where lactic acid (-) contains H on the left and OH on the right.
Try to superimpose the structures in your mind so that they match. If they don't match and are mirror images of each other, then, they are optical isomers.
Look at the chemical structures of trans-2-butene and cis-2-butene. Notice that both structures have the same molecular formula of C4H8.
See the difference of the arrangement of atoms in the structure. Notice that the carbon and the methyl group (CH3) are arranged in different places of each structure.
Notice that geometric isomers contain the same molecular formula, but differ in the structure of atoms around a double bond.