Shore = the area between the sea, lake or river and the land within a local area (for example, within a bay - but a shore can be quite long). Normally, something you can walk on or at least land a boat on (a cliff is not really the shore). "The raft approached the shore". A shore can be a beach, but a shore could be a rocky shore.
The shore extends approximately from the water's edge to the high-water mark (the furtherest the sea can reach). After this point, you are on the land proper.
However, the word can in some contexts also just mean "next to the sea/lake/river". For example: "I have a house on the shore" means your house is next to physical shore as defined above (but not necessarily that it is actually on the beach itself or anything like that).
A shore can be on a lake or a river (unlike coast, which is only used with open water). So shore is equivalent to coast in the context of rivers and lakes. You would only use it for large rivers though; otherwise use "bank" or "riverbank".
It is also used as a general term for "the land", hence "ashore" means on the land, as opposed to at sea. "The ship was heading to the shore" could just mean it was heading towards land. The expression "ship to shore communications" just means "communications between someone on a boat and someone on the land".
Shoreline = like shore, but emphasising the exact border between the water and the land, or emphasising the shore as a long two dimensional entity (perhaps because it is far away). "The shoreline was littered with seaweed" or "the shoreline curved away".
Beach = Shore, but flat and usually with at least some sand or very small stones. The more sand, the better the beach!
Coast = The border between land and sea on a larger scale than shore. Not usually applied to lakes (unless perhaps they are very big). "The north coast of Cornwall is rugged". You don't talk about the north shore of Cornwall (a county in England).
Unlike "shore" the coast can extend inland some way. If you have "a house on the coast" it means your house is within a few kilometres of the sea.
Coastline = like coast, but emphasising the exact border. Often used when talking about the length or shape of the coastline.
Sand = the white or beige material on a beach, on a riverbed or in golf-course bunkers.