What kind of errors were you getting while it was still in the notebook?
Why do you think plugging it into an external enclosure will help?
Generally hard drive errors occur in one of 2 areas. Either a something happens to the external PCB (circuit board), or something happens internally to the heads, platters, spindles, etc.
The PCB is about the only thing you can attempt to repair yourself, and I wouldn't recommend it if the data on the drive is critical. The PCB is generally attached with T9 torx screws, and can be replaced if you can find another drive of not only the same make/model, but firmware. There are sites that specialize in the sale of replacement PCBs.
Finally, if you decide to leave it to a pro, hard drive recovery will probably cost at a minimum $500, and can be in the thousands if the damage is internal.