Look at the disassembly. Almost any C/C++ debugger will be happy to show you the machine code and the registers where the program crashed. The registers include the Instruction Pointer (EIP or RIP on x86/x64) which is where the program was when it stopped. The other registers usually have memory addresses or data. If the memory address is 0 or a bad pointer, there is your problem.
Then you just have to work backward to find out how it got that way. Hardware breakpoints on memory changes are very helpful here.
On a Linux/BSD/Mac, using GDB's scripting features can help a lot here. You can script things so that after the breakpoint is hit 20 times it enables a hardware watch on the address of array element 17. Etc.
You can also write debugging into your program. Use the assert() function. Everywhere!
Use assert to check the arguments to every function. Use assert to check the state of every object before you exit the function. In a game, assert that the player is on the map, that the player has health between 0 and 100, assert everything that you can think of. For complicated objects write verify() or validate() functions into the object itself that checks everything about it and then call those from an assert().
Another way to write in debugging is to have the program use signal() in Linux or asm int 3 in Windows to break into the debugger from the program. Then you can write temporary code into the program to check if it is on iteration 1117321 of the main loop. That can be useful if the bug always happens at 1117322. The program will execute much faster this way than to use a debugger breakpoint.