How to mount a partition from a full disk image

Get the partition layout of the image

$ sudo fdisk -lu sda.img
...
Units = sectors of 1 * 512 = 512 bytes
Sector size (logical/physical): 512 bytes / 512 bytes
...
  Device Boot      Start         End      Blocks   Id  System
sda.img1   *          56     6400000     3199972+   c  W95 FAT32 (LBA)

Calculate the offset from the start of the image to the partition start

Sector size * Start = (in the case) 512 * 56 = 28672

Mount it on /dev/loop0 using the offset

sudo losetup -o 28672 /dev/loop0 sda.img

Now the partition resides on /dev/loop0. You can fsck it, mount it etc

sudo fsck -fv /dev/loop0
sudo mount /dev/loop0 /mnt

Unmount

sudo umount /mnt
sudo losetup -d /dev/loop0