Short answer, to the question title:
Often, a galvanic cell is illustrated as having two electrodes, two electrolytes, a salt bridge, and wires bridging the electrodes to a voltmeter.
The piece missing from your list of components, in terms of a galvanic cell being put to practical use, is the load. You're correct, if a load were attached to the cell, it would be wired in parallel with the voltmeter.
A quick search turns up the following schematic along the lines of your description, from the UC Davis ChemWiki:
From a brief scan, the construction of the half-cells and salt bridge look okay to me. I have not double-checked the half-cell potentials for accuracy.
If I read the schematic correctly, there is no load attached, and so the only thing completing the circuit with the galvanic cell is the voltmeter. In this case, the appropriate cell voltage would be read on the voltmeter. However, the current through the system would be negligibly small, due to the extremely high resistance of the voltmeter. The $\leftarrow e^-$ notation here indicates only the direction that current would flow through a lower-resistive load that were connected (again, yes, in parallel) with the voltmeter.