How to turn an internal hard drive into an external one

I'm looking to repurpose an old internal hard drive into an external one, so I could use some guidance. What kind of enclosure or cables should I be looking for? Here is the specific drive I have in mind:

Seagate ST1000LM035 (SATA), 148 GB, 3.5"

You're looking for a drive enclosure—basically an external bay for a 3.5" SATA drive.
http://www.amazon.com/external-hard-drive-enclosures/b?node=12513281
The enclosure should come with all the cables you'll need.
Just keep in mind—you’ll always need a wall outlet handy since it requires a power adapter.

So, I went ahead and picked up an external enclosure for that specific hard drive. I slotted the drive in, hooked everything up, and plugged it into My PC, but the system isn't recognizing it at all. To be thorough, I even tried connecting it to two different receivers, yet I’m still met with total silence. Before I head back to Best Buy to return this thing and ask for their take, does anyone have any insights?

There are a ton of cases out there. It’d actually be helpful if you just told us which one you grabbed and dropped a link to it...

I am referring to this specific chassis

Once you plug it into your PC, follow these steps:
Right-click on My PC—select Manage—then go to Disk Management.
You should see the drive listed on the right side. It won't have a letter assigned yet. Right-click it and select
Change Drive Letter
Assign it a letter, and it should work just fine.

It isn't detecting the drive at all. Honestly, I’m starting to suspect the Seagate ST1000LM035 might have just kicked the bucket on me—that feels like the only logical explanation left. Though, to be fair, when I lean in close to the case, I can actually hear it spinning, which makes this whole situation even more baffling.

Did you actually plug both internal connectors in? And did you even turn the power on?

Look, I’m telling you, everything is connected properly—I can actually hear the hard drive spinning away inside the chassis—yet it’s nowhere to be found in Disk Management, and no other devices seem to recognize it either. 😠

Try using a different PC and make sure both cables are actually plugged in. I had a total meltdown when I bought a generic external drive enclosure from Best Buy once; one cable only had two wires for power while the other had all four for data and power.