I understand what it means to have an account temporarily suspended, but what happens if I think the suspension was too harsh or unjust?
If I am a new contributor and unfamiliar with how things work on SE, how do I appeal the suspension?
Can a suspension be reduced? How do I do this? Who do I ask?
First of all, if it's your first offense and a minor one, you will usually be warned but not suspended. So either you have been made aware of the rules already, or common sense would have suggested that whatever you did was a bad idea, even though you might not be familiar with Stack Exchange and its rules.
That said, you have the option to reply to the moderator message (via e-mail, or via the message in the inbox in the top bar) to make them aware of things they don't know yet and might influence your case. With the new evidence, they might reach another decision and lift or reduce your suspension. Note that you only have one chance to reply to the message, so be careful to present the evidence in a convincing way.
The last option, reserved for extreme cases (like suspected abuse of ♦ moderator privileges) is to use the Contact Us form; a complaint filed here will be handled by Stack Overflow employees.
See the procedure described above.
Practically, suspensions are a last resort and we'd really like not to have to suspend people. There's often some other stuff going on, a user's overall history and contributions.
While seemingly punitive, by design, suspensions are also meant to be cooling off periods - so a good way might be to actually show that you're aware of what happened, and display a desire to make it right. The first suspension's usually at most a week anyway.
In short a good first step if you're a new user is trying to work out how and why you went wrong. Unfamiliarity on its own isn't a good excuse for breaking the rules. Then you can open up a dialog with the mods, or simply wait it out.
If it's really really bad, and you really need to get a CM to take a look, you can use the contact us link. That said, if you did manage to get the suspension reduced, please do remember the mods are the folks on the ground. If you do the same thing again - you will get suspended and longer.