I used to work for a New Mexico Assessor's office. I believe the laws in CO are similar, but here we go.

In NM

Within the accepted period, you can file a protest. The county will have a period in order to informally arbitrate this protest, during this time, it would be one on one conversations with an county official, negotiating an agreement. If an agreement cannot be made within a period of time, the protest will move on to a formal hearing. In NM the board is made up of a member of NM State Tax and Revenue and several local appointed members (usually they are people connected with the real estate industry) at the formal hearing, both sides will present their info and a decision will be reached by the board. As far as I know, CO is very similar to this.

That being said. There are several ways to approach this when Residential property is concerned. There are two main way to value residental property. Replacement value (including appropriate depreciation) also known as Cost Approach and Market value also known as Sales Approach. Most current appraisal theory states that the sales approach is the most accurate way. Basically, comparable sales (like properties ie same number of bed, bath, style, location, etc) will show what a target property should be worth. The cost approach is better used when there are few comparable sales in order to make a value judgement.

When sale prices are running high, realtors and tax folks love the sales method, while homeowner love the cost approach. When prices are low, its the opposite. The issue with property tax, is that a variety of state laws jump in that interfer with valueing the house at appropriate levels. New Mexico has a great one, search "New Mexico Tax Lightning" for more info. As far as handling a protest, from the property owner standpoint. Understand that your home value is based on an average of what many similar homes to yours are selling for, not what you paid for your particular home. Many times though, the comparable sales have been cherry picked by the assessor, realtor or even property owner. The more comparable sales you can bring to the protest, the more firepower you will have to dispute your value. (assuming that the comparable sales say that your home is overvalued) But if you happened to get a great deal on your home, you might be out of luck, if the comparable sales say that you should have paid more. Searching MLS and even contacting a local realtor are good ways to get comparable sales figures. As for the cost approach, you should know that the replacement cost will be figured again based on average cost to replace something, not what you might be able do it for.

Davsel is correct in looking into the variety of exemptions that are available as well. Many of these are underpublished.