Each carbon in graphite is bonded to three other carbons in a trigonal planar structure. This means that graphite forms in perfectly flat sheets. A block of graphite is actually many many separate layers of graphite (each its own molecule) held together by London Dispersion Forces, or perhaps some imperfections or impurities.
The structure of the molecule can be seen here
Each corner in this structure represents a carbon atom, bonded to three others. In nature, the structure extends the full width of the molecule.
It is important to note that the bonds are not exactly as seen here. A single image (or single Lewis Dot Structure) cannot really show all of the bonds, because this structure is highly resonant. In other words, you would have to draw multiple pictures to show all of the places the double bonds could be, and the truth is that each bond is really somewhere between a single and a double.
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