I'm a software engineer, but I'm not too skilled at understanding hardware design yet. I'm trying to learn how to use an Arduino Pro Mini board without the programmer connected, so I can actually make fun toys, etc. Currently, the software will only run when connected to the programmer (or at a minimum with the SCK pins connected to each other). I have been searching online for days, and I think I need a crystal or resonator hooked up somehow, but I can't figure out how to hook them up (which pins). I bought 5 16 MHz ceramic resonators, and I have them right here with me, but I can't find the answers online how to hook it up and have the board run stand alone. Any ideas? Thank you in advance.
You might be on the wrong track.
You do need a crystal (or not, it depends on), and an Atmel programmer if you want to program an empty chip.
However, all Arduino boards come with a chip pre-programmed with a bootloader. Then it is rather easy: you need an FTDI cable to connect the board to a PC. Then run Arduino IDE on the PC. (The FTDI cable is actually an USB-to-serial converter.)
The Arduino IDE lets you edit a C like code, complile it to binary, and send it out via the FTDI cable to the serial port (Rx, Tx) of the board. The microcontroller on the board comes with a bootloader. Bootloader is a small program which runs at power up, and will receive the data from the computer and put your program to the microcontroller. Then your program will run on the microcontroller.
So, you don't need an external programmer.
On the other hand, you may consider picking a different Arduino board. Arduino Micro, or Pololu A-star Micro (for half of the price of the Arduino Micro) offers a board with a direct USB connection. All you need is one USB cable.
These boards come with a much better microcontroller (32u4) which has a hardware USB connection (allowing you to make a mouse or a keyboard, and control PC (such as buttonbass.com) from your gadget).