First calculate the degree of unsaturation: the result is 1. The compound will have a ring or a double bond.
Since the degree of unsaturation indicates that the compound could have a carbonyl, let's look for that first, since carbonyl bands are strong and distinct. Carbonyls show up in the region 1760-1665, and specifically, saturated aliphatic esters from 1750-1735. Sure enough, there is a band at 1740 indicating a saturated aliphatic ester. There is a possibility that the compound is has both a ketone and an ether group instead of an ester, however, the band at 1740 indicates an ester instead of a saturated aliphatic ketone. You can also see bands in the region 1300-1000 which can indicate the C-O stretch.
We think that the compound is an ester, having the functional group -O-(C=O)-. Let's look at the NMR to get an idea of how many different hydrogens are in the molecule so that we can narrow down the number of possible structures.
The NMR indicates that there are 4 different types of protons in the molecule. The 6 protons at 0.9-1.0 ppm indicate two methyl (-CH3) groups, each adjacent to a carbon which has 2 hydrogens:
These two methyl groups (red, above), situated next to a methylene group (-CH2-), are not very close to an oxygen.
The peak at 4.0-4.1 ppm has two protons, so it is a methylene group. In an ester, hydrogens on a carbon adjacent to the oxygen are from 3.7-4.1 ppm. This leads to the sub-structure below:
The peak at 2.2-2.4 ppm has two protons, so it is a methylene group. In an ester, hydrogens on a carbon adjacent to the carbonyl are from 2.0-2.2 ppm. This leads to the sub-structure below:
Let's line up the substructures we have so far:
If we join the sub-structures as indicated, we have accounted for all 7 carbons. The un-colored protons above must be the 4 hydrogens in the sextet from 1.6-1.8 ppm. This makes sense, since these hydrogens are adjacent to both a carbon with 3 hydrogens and a carbon with 2 hydrogens. Here is the proposed structure with these 4 hydrogens shown in purple:
This is how the structure correlates with the NMR:
Example 4 is propyl butanoate:
Note: the nomenclature of esters is discussed briefly in the section on esters.