Need help understanding range of a linear tansformation

[eyehategod]

I've been reading my book on finding the range of a linear transformation but can't understand it. Let's say:
T(x)=Ax
then the range(T)=columnSpace(A), right?

But I've gotten confused so much about columnspaces b/c I've read many books and websites that explain it differently from each other. Can anybody explain to me in plain English how to find the columnspace(A) so I can find the range(T). Thanks in advance.

 

[EnumaElish]

In linear algebra, the column space of a matrix is the set of all possible linear combinations of its column vectors. The column space of an m × n matrix is a subspace of m-dimensional Euclidean space. The dimension of the column space is called the rank of the matrix.

http://en.wikipedia.org/wiki/Column_space

See also: http://mathworld.wolfram.com/ColumnSpace.html