Klinefelter syndrome is 47, XXY (although this syndrome could have had as many extra X's as you want which would increase the total number of chromosomes) with one Barr body (or more if there were more than two X's)
XYY syndrome is 47, XYY (easy!) with no Barr body.
Turner syndrome is 45, XO (some folks include the "O" and some don't) and she will have no Barr body (just like an XY guy).
Trisomy syndrome is 47, XXX with two Barr bodies.
As you look over this list remind yourself of the sex of each of these people by recalling that "if it has a Y it has to be a guy".
Also notice that everyone has at least one X chromosome.