Compare and contrast the process of mining coal and extracting oil ?
Very different actually.
There are many ways of mining coal. They all have the same basic concept, so I'll focus on one.
Mountaintop removal is used for all sorts of mining purposes, but is frequently used to extract coal in Appalachia. Miners literally use explosives to blow off the tops of mountains to reveal deposits of ores, which they extract, and then process by usually filtering them through substances such as mercury to purify them somewhat. Mining coal is a lot like mining any other metal or ore, it's just processed differently.
Oil extraction is much different because oil is a liquid, not a solid like coal. There are many different ways of extracting it because oil is found in very diverse forms such as shale, liquid oil deposits, etc. I'll focus on the liquid since that is pretty common.
Rock below the surface varies in level, but aquifers, where present, tend to remain the same level because of gravity. Since oil can sometimes be present near aquifers, it will float to the top, and often finds where the rock is higher up to gather in small pools floating above the water table. People looking for oil will often find these places and drill down. Since oil is a liquid, if you drill down to the source, you can pump it out. People also use fracking (where you drill down and pump water and other chemicals to increase oil flow) to extract oil out of a drying reservoir.
Overall, two very different processes. One thing they have in common is the environmental impacts. The mining is extremely harmful to the environment, as is fracking and oil wells because both destroy habitat and introduce extremely harmful chemicals to surface water, groundwater, and soil.