extend size of partition
You don't need to turn off the swap partition because it is before the /dev/sda3 partition. Run fdisk to extend the end of partition 3 further. You may have to delete and recreate it, but as long as the start stays the same and the end is >= where it currently is, that will work.
Extending the filesystem depends on which FS you already have installed. For ext2/3/4, you'll typically use resize2fs.