How can I invoke buffer overflow?

That is compiler dependent, so no single answer can be given.

The following code will do what you want for gcc 4.4.1. Compile with optimizations disabled (important!)

#include <stdio.h>
#include <stdlib.h>

void g()
{
    printf("now inside g()!\n");
}


void f()
{   
  int i;
  void * buffer[1];
  printf("now inside f()!\n");

  // can only modify this section
  // cant call g(), maybe use g (pointer to function)

  // place the address of g all over the stack:
  for (i=0; i<10; i++)
     buffer[i] = (void*) g;

  // and goodbye..
}

int main (int argc, char *argv[])
{
    f();
    return 0;
}

Output:

nils@doofnase:~$ gcc overflow.c
nils@doofnase:~$ ./a.out
now inside f()!
now inside g()!
now inside g()!
now inside g()!
now inside g()!
now inside g()!
now inside g()!
Segmentation fault

Since this is homework, I would like to echo codeaddict's suggestion of understanding how a buffer overflow actually works.

I learned the technique by reading the excellent (if a bit dated) article/tutorial on exploiting buffer overflow vulnerabilities Smashing The Stack For Fun And Profit.

While this solution doesn't use an overflow technique to overwrite the function's return address on the stack, it still causes g() to get called from f() on its way back to main() by only modifying f() and not calling g() directly.

Function epilogue-like inline assembly is added to f() to modify the value of the return address on the stack so that f() will return through g().

#include <stdio.h>

void g()
{
    printf("now inside g()!\n");
}

void f()
{   
    printf("now inside f()!\n");
    // can only modify this section
    // cant call g(), maybe use g (pointer to function)

    /* x86 function epilogue-like inline assembly */
    /* Causes f() to return to g() on its way back to main() */
    asm(
        "mov %%ebp,%%esp;"
        "pop %%ebp;"
        "push %0;"
        "ret"
        : /* no output registers */
        : "r" (&g)
        : "%ebp", "%esp"
       );
}

int main (int argc, char *argv[])
{
    f();
    return 0;
}

Understanding how this code works can lead to a better understanding of how a function's stack frame is setup for a particular architecture which forms the basis of buffer overflow techniques.

Try this one:

void f()
{   
    void *x[1];
    printf("now inside f()!\n");
    // can only modify this section
    // cant call g(), maybe use g (pointer to function)
    x[-1]=&g;
}

or this one:

void f()
{   
    void *x[1];
    printf("now inside f()!\n");
    // can only modify this section
    // cant call g(), maybe use g (pointer to function)
    x[1]=&g;
}