Several ways really PP: on a simpler front, there will be liner notes either in the booklet, or on the cover that will tell you it's remastered, or that so-and-so remastered at such-and-such studio (Metropolis is a common one in London, SOundkeeper is Barry Diament's but rarer, then the likes of Peter Mew at Abbey Road who did the recent Deep Purple Machine Head 40th Anniversary remaster, etc, etc). These days, it's usually plastered all over it in some form or another.
Your Tracy Chapman one - if it's on the WEA group (Warners-Elektra-Asylum) - will probably have the little silver "Digitally Remastered" sticker on the front and the jewel case will show the grey strip on the inner spine facing bearing the same words. The catalogue number might also be different - I think WEA mostly start 7599- and then the rest. The original versions were often just a five digit cat number, hyphen and then a single digit afterwards (this is WEA again).
Some remasters will be very obvious tonally, the Genesis ones from 2007 being the most criminal, while others less so (Springsteen's Born to Run 25th Anniversary looks like the tapes were walked past a mixing desk but not much else, see also the brilliant Japanese remasters you could pick up for a song in HMV a couple of years ago. Procul Harum's mini-vinyl editions on Union Square from two or three years back are similarly well treated.
For the dedicated, there's also the Steve Hoffman site; that's my go-to resource in most cases.
So you've a few options.
EDIT: One other good one on the early WEA CDs again was the note on the rear cover of the CD - "...the high resolution of compact disc might reveal flaws in the original analogue source tape..." or words to that effect. Classic.