The first thing is to know that your timeshare is only worth what someone is willing to pay for it. To this end, you can figure out what your timeshare is worth by placing a bunch of for-sale ads, and asking potential buyers to "make an offer." The responses you receive will give you a rough idea of the timeshare's market value.
If you don't get many responses to your ad, or the responses cover a huge range of prices, the next thing you can do is hire a licensed broker to evaluate your timeshare. Be wary of timeshare brokers who charge a hefty upfront fee for an appraisal, especially if they make no guarantee of selling. And always check their credentials.
Another way to come up with an appraisal of your timeshare's fair market value is to browse ads for condo, townhouse, or hotel room timeshares that are similar to your own. What is the average price of a timeshare in your location? During your week? What is the average selling price of a unit similar in size?
If you like making spreadsheets, this can be fun to do in Excel. Keep in mind that many people who sell timeshares by owner have no idea what to sell for, so take a large enough sample size.
Know the factors of timeshare depreciation and deduct accordingly from the developer's price. Typically, you can expect at least 20% depreciation right off the bat. Then another 10%-20% if the resale market is saturated with units like yours. Expect 10%-20% for having an off-season week, and another 10% if timeshare owners in your resort have little say in how the property is managed.
For example, if the resort sells units like yours for around $15,000, and you calculate the depreciation rate to be around 20+10+10+10 = 50%. That works out to a resale value of $7,500.
Each method gives you a different rough estimate. To get the most accurate appraisal, you should compare all the estimates that you calculate.