Ok, so you don't have a palace with a room covered in amber like this one in the Catherine palace in Russia but, you still want to know if the amber you have or are considering buying is the real deal...here's the inconclusive tests I found to share with you:
1. If it feels warm it's real 2. If it floats in salt water it's real 3. If when vigorously rubbed it has a static charge it's real. 4. If you can make a scratch mark on it - it's real 5. If you can smell it -- it's real 6. We don't recommend this one - heat a needle and press it against the amber if it went in only slightly and smells like old punted tree it's real.
I know none of these are that conclusive but that's usually the case with most gemstones also. So my advice if you love it, buy it...if you're buying it for an investment don't buy it!