You have three options for dealing with a fine. First, you can pay it. The situation will be over and done with. That said, if you make the same violation in the future and have to pay again, your argument for opposing the fine will be weaker, because you've already paid it once, and essentially admitted guilt.
Your second option is to try asking for a variance, which is an exception to the deed or covenant by which your HOA functions. Sometimes, especially if the HOA doesn't want a legal battle, the variance will be granted. In many cases, the HOA will hold a hearing to which other homeowners are invited, to discuss whether or not to grant or deny the variance [source: FindLaw].
Your final option is taking legal action but this should be your last resort. It is possible to win a lawsuit, and sometimes the HOA will have to pay your legal fees [source: Hutcheson]. But homeowners have taken associations to court over hundreds of dollars only to come back, head in hands, owing the HOA the original fines or dues plus thousands of dollars in lawyers' fees.
The worst thing to do is simply refuse to pay the fines without telling your HOA why you're not. You could risk foreclosure, and considering the hard-playing reputation HOAs have, it's better not to tempt fate.