Here's my setup:
Components;
SETUP Hardware required:
PC with soundcard and soundcard drivers loaded (some modern motherboards come with 16 bit sound and that may suffice).
Tapedeck connected to:
Amplifier (Amplifier is optional - see below)e
Amplifier headphones out jack connected to
stereo jack adaptor regular size to mini jack size
stereo minijack and cord connected to line-in receptacle of sound card.

SETUP: Software required:
I am using CoolEdit Lite but unfortunately CoolEdit has been purchased by Adobe which has offered their version of the software in an expensive one version only. You may have audio software already which came with your CD burner or DVD burner. Nero has a version. There is an open-software version available over the net called 'Audacity'. I have it for linux but haven't used it much.

If you have a tapeplayer but no amplifier, you may use either the headphone output jack of your tapeplayer or the output RCA jacks on the back, using a patchcord which has RCA at one end and a minijack on the other.

PROCEDURE:
I am digitizing many kinds of tapes, classical prerecorded stereo with Dolby to mono personal voice messages. So I play a tape into my computer, set it on record, and view the output in the software, which brings up a kind of 'oscilloscope' signal in windows for Left and Right Tracks. I have to adjust for maximum volume, I want the maximum volume of the signal to go the maximum limit of the software for signal to noise reasons (exactly the same principle as if I was converting an LP to tape). I have also found that even on high quality prerecorded classical cassettes, that left track and right track may need level adjustments, and one side of a cassette may not match the other side.

Unlike the procedure of converting LPs to digital, tapes do not skip, do not crackle or pop. I check for Dolby. If the tape isn't Dolby, I do not play it back Dolby. I personally do not know of any 'corrective' software to make the tapes sound better. I takes 'em as they is and there's a lot of good music on them, even if they are not Dolby, even if they are 45 years old.

If I'm converting music, I sample stereo at 44,100 Hz. If it is spoken word, I may reduce it to mono at 22,050.

A lot of it may get converted to mp3 or aac, but I've got a large hard drive dedicated to storing the stuff. Rough order of magnitude: 1 hour of stereo hi fi will fit into 1 gig of memory.

Clear as mud? E Mail me.
Did I say somethin' stoopid? Please let me know as I'm intending to do this to a couple hundred cassettes.

Meanwhile, my cassettes have held up very well. CDs and DVDs are less certain. I think there is more confidence in them out there than is warranted. Magnetic storage has proven to be very good. I would even venture to buy an additional hard drive as backup, and turn out CDs as needed but maintain the info on the hard drive. As time goes on, today's DVDs will give way to other even denser media.