I was asked this a while ago, and then again today. Basically the question is "If global warming is causing the icebergs to melt, and 95% of an iceberg is below the water already, then how can this cause sea levels to rise so much?"
It is true that when water expands as it freezes and this is how the grand canyon formed millions of years ago (well, that and a little bit of erosion), but lets not get carried away here. The shrinkage from ice to water is only 0.41%
This means that if you have a litre bottle full of the purest ice water, it would shrink to 995.9ml (almost a teaspoon).
Also, lets look at your typical iceberg. Approximately 7/8ths of the iceberg are below the water. So, lets demonstrate with a theoretical 8 litre iceberg. Lets split into the gains and losses above and below the water.
Above the water
Total volume: 1 litre
Loss on melting: 4.1ml
Below the water
Total volume: 7 litres
Loss on melting: 28.7ml
Although the ice that was below the water reduces in volume, the water that was ice above the water cannot hover, the 995.9ml from here is added to the water in the sea. Therefore, although you are loosing 28.7ml of volume, you gain 995.9ml, so a resultant net gain of 966.9ml.
Consequently for every 8 litres of iceberg, you gain 966.9ml of water level rise.
By the way, there are quite a few factors that influence the freezing process - density of water based on purity, pressure, ambient temperature etc, but this example should demonstrate that even if you go to the extremes of the error margins - icebergs melting = water levels rising.