Just use any available interrupt-driven serial code.

Get first character from receive buffer.
If parameter is expected for that character, retrieve characters one at a time and place in a text bubffer until you get a white character or newline character. Then convert the parameter to binary.
If you did get a white character - continue to eat characters util you have processed a newline character. Then you are ready for the next command.

See the links to the left on this page for sample code to handle the serial port.

What compiler do you use - you need a compiler that comes with floating point emulation if you are gooing to work with floating point values. The alternative is to write your algorithm so that it uses fixed-point arithmetic.