Hi Violagirl,
Coupling constants
When you have peak multiplicity (such as doublets and triplets), this is due to a neighboring atom coupling with your proton. Most often, it is due to another hydrogen atom in the vicinity. By determining coupling constants of your protons in your system, you will be able to figure which protons are near each other.
For exemple, if you have a doublet with a J value of 8.4Hz, you should be able to find another set of peaks with a multiplicity of 8.4Hz, meaning that these protons are near each other. This will give you a set of clues about the structure of your molecule.
Integration
If you have multiple peaks in an NMR spectra, the integration gives you a ratio between those peaks.
For exemple, if a peak integrates for 2 and a second for 3, it can also mean you have 4 hydrogen atoms of one type, and 6 of another type. However, if they did not give you the molecular formula, it is more than probable that these integration will be right on.
In the early days of NMR spectroscopy, integration ratio was obtained by cutting and weighing the paper on which the spectra was printed on. I heard that this was a fairly acurate method...
I hope this helps