Note: this technically only applies to land in the UK and Ireland, but these concepts are still valid legal buttressing for any "get off my land" situation where you want rid of a trespasser, mother in law or door to door religious pilgrim.
Let us begin with the physical dimensions:
The actual physical surface of the ground is obviously the first thing we look to, this is first legal dimension of land. The next is any physical building on the land, derived from Elitestone v Morris - "any physical buildings on the land are part and parcel of the land itself." Following on from this, any objects attached to the land are also a legal dimension of it. In order to define whether an object is "attached" to the land we must look to the rather unusual situation arising in Holland v Hodgson. Here the house in question was resting on four stone pillars which were embedded in the earth. The house was not attached to said pillars, merely resting on them. It could be argued that the house was therefore not attached to the land and not legally a part of it. However, it was pointed out that the house could not be removed without destroying it. We can therefore conclude that it was a fixture of the land.
To summarise: items which cannot be removed from the land without damaging or destroying them are known as fixtures and are a legal dimension of the land. If something can be removed without harm coming to it, it is a chattel.
Having so far dealt with the land and the structures on it, we must now consider the airspace above the land and the ground below it. You do own the air above your land, but only up to a point. Two contrasting cases supply us with the legal airspace paradox. In Bernstein v Skyviews, the then director general of the BBC was somewhat irked by the pilots at Skyviews taking aerial photographs of his property, which they subsequently tried to sell to him. He was granted an injunction preventing Skyviews from invading his airspace. However, whilst it might seem that the courts upheld Bernstein's request that they "keep off my air", the judges also pointed out that landowners have "no indefinite right to airspace". This was reinforced by Pickering v Rudd. Here it was stated that you can fly a balloon over someone's land freely, but should the balloon fall, you are a trespasser.
The law governing the subterranean strata below the surface of your land is much simpler and is defined by statute. Any treasure, minerals, artifacts, or petroleum you may find in your back garden belongs to Her Majesty's Government.