To use it, you need an eSATA data cable (eSATA to eSATA) that connects the drive to your computer. I can't see the picture well, but considerng the number of cables that came with your Lacie drive, I believe one of them is an eSATA cable.
This cable runs from the back of your external to your computer. There may or may be an eSATA port on the back of your computer. Check the back (and front) of your computer to see if you have one.
If you don't have one, you have two options. One, get an eSATA "bracket", and the other to get an eSATA "card" both of which will give you an eSATA ports on the back of your computer.
If you get an eSATA bracket, inside your computer, you connect the bracket to "SATA ports" on the motherboard of your computer.
Here are some examples of eSATA brackets.
http://www.newegg.com/Product/Product.aspx?Item=N82E16812104063
http://www.newegg.com/Product/Product.aspx?Item=N82E16812816068
If you have some SATA ports available on your motherboard, this is plausible.
If you get an eSATA card, the card goes into a PCI slot, so you need an available PCI slot on your motherboard.
PCI slot: http://www.newegg.com/Product/Product.aspx?Item=N82E16815158167
PCI Express 1.0 slot:
http://www.newegg.com/Product/Product.aspx?Item=N82E16815158093
http://www.newegg.com/Product/Product.aspx?Item=N82E16815158088
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