Question

How may I read NMR splitting?

Answer 1

Coupling constants
For proton NMR (in which there IS splitting), you can find coupling constants (J in Hz). The peak separations of noticeably separate peaks (such as doublets, doublets of doublets, etc.), if currently in ppm, can be converted to Hz by multiplying by the operating frequency of your NMR spectrometer in MHz.
EX: if it's 300 MHz, then 0.027 ppm = 8.1 Hz

You can look up references that tell you what the coupling constants indicate in terms of what protons are interacting ("talking") with each other. For example, you often see ~8Hz coupling constants in ortho splittings in aromatic compounds like toluene and styrene.

Possible process
From similar coupling constants (within maybe 0.5 Hz is fine), you can try to match up which protons are talking with which protons, and build a structure from there. But, it would be nice to have an IR spectrum with that to give you an easier basis to work off of in terms of finding out what the general structure could be.

Splitting considerations
Recall that, for example, triplet splitting is due to two proton neighbors, but doublet-of-doublet splitting is probably due to a combination of ortho (J ≈ 7~9 Hz) and meta splitting (J ≈ 2~4 Hz or so) on aromatics. Also recognize that occasionally, if you have bad peak resolving, you may have a "faux" triplet that is actually a not-fully-resolved doublet of doublets; watch for subtle peak shoulders.