Assuming the disc was partitioned with a halfway modern Operating system, the first partition should start at 1 MB (sector 2048). In a hex editor, you should be able to see immediately if this is the case, as for example in NTFS you'll see the string NTFS amongst the first few bytes. In an NTFS, on byte 0x28 of that sector you'll find the size of the file system in sectors (little endian, 8 bytes). Add these to the 2048 sectors and you'll know where the end of the partition is. Usually, at the end point you'll find an exact copy of the sector 0 of the partition (not the disk).
After this address, you can now search for the 2nd partition, if that also was an NTFS partition, simply searching in a Hex Editor for "NTFS" as string will suffice, you'll then find (usually within the next MB) the start of the 2nd partition.
If the filesystem is ext2/3/4, you'll see nothing at the start of the partition, as the ext2/3/4 data only starts 1024 bytes (= 2 sectors) inwards.
Also, if the disk was partitioned with Windows XP (or older Linux fdisk), the first partition might not start at 1MB, but rather on sector 63.