Here is one way - very in accordance with the documentation on ImageTake[]:
(* example-image: *)
img = ImageResize[ExampleData[{"TestImage", "Bridge"}], {626, 623}];
{xdim, ydim} = ImageDimensions[img];
col1 = Round[(xdim - 256)/2];
col2 = col1 + 255;
row1 = Round[(ydim - 256)/2];
row2 = row1 + 255;
img1 = ImageTake[img, {row1, row2}, {col1, col2}]
ImageDimensions[img1]
ImageCompose[img, ImagePad[img1, 1, Red]]
