I would suggest talking to an accountant. You are going to want to get a number for this that best serves your tax needs. I know that accountants can use several methods of valuing property based on its original purchase price for tax purposes that can often be much more advantageous for the tax payer. The bottom line is you want to find something that is a) acceptable to the IRS and b) gives you the very best advantage as far as your taxes are concerned. If you have owned the property for a long time, either the county or accounting methods are likely to give you a number that works well for you.
You are in a tougher spot if you bought when the market was high. Your best bet in that case (depending on what the IRS will accept, if a brokers opinion of value is enough for them, do that), you might want to request a re-assessment from the county. You have to file for this before September and the fee is $30 (or at least it was when I looked it up a few months ago).
I have included a link for the part of the assessors office where you ask for a re-assessment.
To determine the "market value" of your home, you can hire a licensed, local appraiser or you can contact a local Real Estate agent who can provide you a market analysis to determine the approximate market value of your home.
Not sure if you are looking to determine value for something specifically relating to the filing of your taxes, for such things as Homestead Exemptions or to determine whether or not you have to pay Capital Gains, or whether it is related to one of the above descriptions I've noted above, but the question is a bit vague.
Hope this helps!
I would recommend that you hire an appraiser to assess the value of your home. Make sure that the appraiser has experience in your area. Do NOT hire an out of area appraiser. There will be a cost for this service. If I may be of further help please let me know.
It also depends on who you are trying to prove this too. You should ask them what they need to determine the value. In many cases a brokers opinion of value will do. In others, they will want you to get an appraiser.
Hope that helps,