How does a voltaic cell produce an electric current?

An electric current is a flow of electric charge.
Electric currents can be produced through the movement of electrons through a wire.

When we think about the movement of electrons, we usually think redox reactions, or reactions which involve a transfer of electrons.
Let's take a look at this redox reaction:

#Zn + Cu^(2+) -> Cu + Zn^(2+)#

We can see that the oxidation state of #Zn# changed from #0# to #+2#, which means that it's been oxidised, or has lost electrons.
We can also see that the oxidation state of #Cu# changed from #+2# to #0#, which means that it's been reduced, or gained electrons.

In other words, #2# electrons were transferred from #Zn# to #Cu#.

Normally, when this reaction happens, electrons are transferred directly between the two reactants to form the products.
That's not really helpful if we want to conduct an electric current.

So, a voltaic/galvanic cell separates #Zn# and #Cu#, and uses a wire to connect them:

The electrons can't be directly transferred anymore.
This results in electrons moving from #Zn# to #Cu# across the wire to make the redox reaction happen.

And as these electrons are moving across the wire, an electric current is produced.

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In a voltaic/galvanic cell, we also see the use of a salt bridge or porous disk to allow ions to flow between them.

This is basically to maintain charge. We won't get into it right now because it's not too relevant, but more about salt bridges/porous disks here!