The easiest to use option -shave Nwill remove a depth of N pixels from each edge of the image.
For instance:
convert \
original.gif \
-shave 30 \
result.gif
This will allow you to shave out 30 extreme rows / columns of pixels from each edge of the original image.
PDF (, PNG):
convert \
some.pdf[0] \
-scale 25% \
-shave 30 \
result.png