If you have a MBR partition table, you can use fdisk:
sudo fdisk -l
This command will print out the partition table and will also automatically perform some consistency checks. If instead you have a GPT partition table, you can use gdisk (thanks Rod Smith for pointing that out):
sudo gdisk /dev/something
where /dev/something is the path to your disk device file (e.g. /dev/sda). From the gdisk interface you will be able to press v to run consistency checks.
About the filesystem, there are many ways to perform the check, the one I prefer is this:
sudo touch /forcefsck
This way, once you reboot the computer, the filesystem is checked for errors. This is a nice way of doing it because you don't need to worry about the dangers of running fsck.
It's worth noting that the file /forcefsck will be automatically deleted as soon as the check has completed.