Under Linux, you can get mount point information directly from the kernel in /proc/mounts. The mount program records similar information in /etc/mtab. The paths and options may be different, as /etc/mtab represents what mount passed to the kernel whereas /proc/mounts shows the data as seen inside the kernel. /proc/mounts is always up-to-date whereas /etc/mtab might not be if /etc was read-only at some point that wasn't expected by the boot scripts. The format is similar to /etc/fstab.
In both files, the first whitespace-separated field contains the device path and the second field contains the mount point.
awk -v needle="$device_path" '$1==needle {print $2}' /proc/mounts
or if you don't have awk:
grep "^$device_path " /proc/mounts | cut -f 2
There are a number of edge cases where you might not get what you expect. If the device was mounted via a different path in /dev that designates the same device, you won't notice it this way. In /proc/mounts, bind mounts are indistinguishable from the original. There may be more than one match if a mount point shadows another (this is unusual).
In /proc/self or /proc/$pid, there is a per-process mounts file that mimics the global file. The mount information may vary between processes, for example due to chroot. There is an additional file called mountinfo that has a different format and includes more information, in particular the device major and minor numbers. From the documentation:
36 35 98:0 /mnt1 /mnt2 rw,noatime master:1 - ext3 /dev/root rw,errors=continue
(1)(2)(3) (4) (5) (6) (7) (8) (9) (10) (11)
(1) mount ID: unique identifier of the mount (may be reused after umount)
(2) parent ID: ID of parent (or of self for the top of the mount tree)
(3) major:minor: value of st_dev for files on filesystem
(4) root: root of the mount within the filesystem
(5) mount point: mount point relative to the process's root
(6) mount options: per mount options
(7) optional fields: zero or more fields of the form "tag[:value]"
(8) separator: marks the end of the optional fields
(9) filesystem type: name of filesystem of the form "type[.subtype]"
(10) mount source: filesystem specific information or "none"
(11) super options: per super block options
So if you're looking for a device by number, you can do it like this:
awk -v dev="$major:minor" '$3==dev {print $5}'
awk -v dev="$(stat -L -c %t:%T /dev/block/something)" '$3==dev {print $5}'