how do both parts of the seat come off my suzuki sv650s?

Answer 1

1) pull off the to small black triangular covers located just below the seat at the gas tank, 2) use your ignition key to unlock the rear seat pillion, once you unlock it it just pops off, 3) unscrew the two bolts that hold on the front part of the seat and lift it at the gas tank end. You should be done!
Reassemble in reverse.

Answer 2

Always give year, make, engine size and model # when asking questions. We need all of that info to research your question.
2003 model - the seat lock is on the left side of the bike below the seat.