Our first step is selecting a Hard Drive Enclosure; the main thing we need for starters is the TYPE of connector you want to use (see above for identifying what you have). After you know the type of connector that you have, lets head over to the External Enclosure section over at Newegg.com. From here, select the type of connector you want to enter either "USB" or "1394" in the keyword box (the dropdown box has options for a lot of combinations, as we could care less and want something that just HAS the connection we're looking for, we'll use the keyword search).
From here, select "Most Reviews" from the dropdown to the right (by default it will say "Best Match"). After all, we do want something reliable don't we...
Now, there will be several options, some cases will require an external power source, others will power themselves from your USB/FireWire port. I'd recommend an external power source one, so you can select "yes" from the "AC Adapter" dropdown; you'll probably also want to select "3.5" from the "Size" dropdown. You can also select the internal interface as well, I'd go with SATA.
From here you'll have a list of the most reviewed external enclosures, select one that looks good for your needs and let's proceed.
Now that we've selected our case, we need to find a hard drive... On the steps selecting our case we may have selected an Internal Interface; if you did not, simply just go to the Specifications page on our case and locate the "Internal Interface" section.
Now, head over to the Internal Hard Drive section of NewEgg.com and select the "Interface" of what your case supports (see the above step); you'll also want to select a size of 3.5". Simply select "Most Reviews" from the dropdown to the right, and find a hard disk you want to use for your new enclosure.
After here, we slide open our External Enclosure, connect our hard drive, close the case, plug it into our computer, and your computer should recognize and install it as a new external hard drive.
Please note that some external cases will list a max capacity, this should be listed on the specifications page, and you should not install a drive larger than it wants.
Note - As SATA3g and ATA133 are backwards compatible with their predecessors, you should have no problem putting them into a system as they will be read regardless of their faster specs. However, SATA and ATA themselves are NOT the same types of drive, thus you cannot put an ATA drive into an SATA slot (it wouldn't fit in the first place).