Sea Level Rise due to Climate Change
The first part of the association is that increasing levels of greenhouse gases in the atmosphere will cause rising temperatures on earth. Here is some information on why that is so, if you are interested. Now assuming that temperatures are currently going up (they are), there are two mechanisms that will connect this to rising sea level, melting of ice on land, and thermal expansion of water  

Land Ice

As climate lawyers are quick to point out, if floating sea ice melts, it doesn't really change the level of the ocean (much) because floating ice displaces a volume equal to an equivalent mass of water. As we will see in the next part, the temperature change from ice melting and then warming will cause some changes. 

Meanwhile, there is about 2.8 million cubic km of ice locked in Greenland's ice cap and 26 million in Antarctica. These two sheets, if fully melted would cause about 7m and 58m of sea level rise, respectively. They will not melt immediately; while the topic is under debate, Greenland will probably take a millennium to melt completely. Antarctica is larger, colder and more isolated from world temperatures fluctuations due to the circumpolar currents, and would probably take a much longer time to melt fully. 

Thermal Expansion of water

The density of seawater changes with temperature. Using data from this chart (Data-Table 9), the density of seawater (at 35000 ppm salinity) at 10 C is $1.0270 \frac{\text{g}}{\text{cm}^3}$ and at 15 C is at $1.0260 \frac{\text{g}}{\text{cm}^3}$. Therefore, there is an estimated $\frac{1.027-1.026}{5} = .001 \frac{\text{g}}{\text{cm}^3}$ change per degree C, or a $\frac{.001}{1.027} = .097 \% $ increase in volume for a one degree C increase in temperature from 10 C to 11 C.

Not all the earth's ocean's are at 10 C, but using this as an estimator, the $1.35 \times10^9 \text{ km}^3$ will increase by $1.31 \times10^6 \text{ km}^3$ with a 1 C increase in temperature. If you divide that by the surface area of the ocean, 510 million $\text{ km}^2$, you get an approximately 2.5 meter increase in sea level.

That calculation is not at all rigorous; deep ocean water is colder than 10 C and at lower temperatures thermal expansion is much less (just look at the linked chart to see), but it does demonstrate that there will be a detectable rise in sea level from thermal expansion of seawater as the planet heats up.