Two things to learn:
1. Learn to recognize electrons that are in identical magnetic environments
2. Learn to generate Pascal's Triangle.
http://en.wikipedia.org/wiki/Pascal%27s_triangleThen for any proton, count the number of protons that are either on the same carbon or on adjacent carbons that are identical to each other.
N adjacent identical protons will split your proton into
N+1 peaks, with integrals according to Pascal's triangle. (Unless the peaks are fairly broad, intensities can usually be substituted for integrals)
So if there are no protons on carbons adjacent to the proton you are considering, there will be 1 peak.
If there is one proton on a carbon adjacent to the proton you are considering, there will be 1+1 or 2 peaks, with the same intensity (a doublet, 1:1)
If there are two identical protons on a carbon adjacent to the proton you are considering, there will be 2+1 or 3 peaks, the center peak being twice as tall as the outside two (a triplet, 1:2:1)
If there are three identical protons on a carbon adjacent to the proton you are considering, there will be 3+1 or 4 peaks, the two middle peaks being three times as tall as the two outer peaks (a quartet, 1:3:3:1)
And so forth.
If there is more than one non-identical proton on a carbon adjacent to the one your proton is attached to, each of them will show its affect separately.
For example:
If you have one proton on the right side of the proton you are considering, and a different proton on the left side, you will see a doublet of doublets - that is, one proton will split your proton into two peaks of equal intensity, and the other proton will split each of those peaks into two peaks of equal intensity.
If you have one proton on the right side of the proton you are considering, and two identical protons on the left side that are different from the one on the right, you will see a doublet of triplets (or a triplet of doublets, depending on which one has the largest coupling constant).
And so forth.
Some examples:
CH
3-O-CH
3 (dimethyl ether) - this compound shows only one peak in the NMR. All of the protons are identical, and none of them are next to any non-identical protons, so it will be a singlet.
CH
3-O-CH
2-CH
3 (methyl ethyl ether) - this compound shows a singlet for the methyl group on the left. All three of the protons are identical, and there are no protons on an adjacent carbon. The methyl group on the right will be split into a triplet, however. There are two protons on an adjacent carbon, which will split the methyl group protons into 2+1 peaks, with intensities of 1:2:1. In return, the two protons on the methylene carbon (the -CH
2-) will be split by the three protons on the adjacent methyl group into 3+1 peaks, with intensities of 1:3:3:1. The methylene carbons will not split the protons on the far right methyl group, because they are not adjacent - there is an oxygen atom in between.
CH
3-CH
2-O-CH
2-CH
3 (diethyl ether) - here the two sides of the molecule are identical, so there is no difference between the methyl group on the left and the methyl group on the right. They will form a single peak. Each proton on a methyl group is adjacent to two protons on the methylene group, so it will be split into 2+1 peaks, with intensities of 1:2:1. The methylene protons will also form a single peak, each proton on a methylene group is adjacent to two protons on a methyl group, and will be split into 3+1 peaks with intensities of 1:3:3:1.
Go back and look at all the compounds at the beginning of your textbook that were used for examples when you were first learning how to name structures, and practice assigning splitting patterns to each of the protons on those molecules.