Yes it's hard to help out without more information
The basic compile command is something like this:
zcc +zx -vn prog.c -o prog.bin -lndos -create-app
The "+zx" selects the z80 target. In this case "zx" is the Sinclair ZX Spectrum and this tells the compiler to use library code written for the Spectrum. You mentioned the intended target is one of the calculators for which there are several possibile targets "+ti8x", "+ti82", "+ti82ansi", "+ti83", "+ti83ansi", "+ti85", "+ti85ansi", "+ti86", "+ti86ansi" depending on which model calculator you are compiling for. I imagine the main difference between them is the graphics code. The ansi libraries include some terminal emulation for stdout.
"-vn" indicates a silent compile (verbose no). "-lndos" links to the stdio library stubs. Many targets do not have disk drives, etc, so cannot have a full stdio implementation. This stdio stub is for such targets. "-create-app" does not work for all z80 targets; this option invokes "appmake" which uses the output machine code to generate a standalone file appropriate for emulators (or whatever) on the intended target. For example, on the ZX Spectrum this option creates a "tap" file which is an electronic image of a tape containing the output binary. "appmake" only supports a finite number of z80 targets and may not be able to do anything for the ti calcs (I don't know but if it doesn't you are welcome to add support!). Regardless of whether or not you can use appmake, zcc will always output the raw binary result.
You would also need to link to more libraries on the compile command if you use them, just like modern C compilers. Eg, if your program uses floating point math you'd need to link to the math library "-lm", etc. Many functions are automatically linked when you specify the target "+zx".
As you can tell I don't have any particular knowledge of the ti ports
Stef did the ports and I don't know what the state of them is. However he has written a brief ti-intro in the wiki which you should check out before doing anything: