Microelectronics' high-performance STM32F429IGT6 microcontroller is built around the ARM Cortex-M4 core. Here's a general guideline on how to connect it in a circuit: 

1. Power Supply: First, you need to power the STM32F429IGT6. The chip operates at a voltage range of 1.8 to 3.6 volts. You should connect VDD pins to a power source within this range, and the VSS pins to ground.

2. Boot Mode: The boot mode is determined by the state of BOOT0 and BOOT1 pins at startup. For regular operation, BOOT0 should be connected to ground.

3. To reset, join the NRST pin to a pushbutton that, when pressed, connects to ground. A pull-up resistor between NRST and VDD will ensure that the pin stays high when the button is not pressed.

4. Oscillator: The STM32F429IGT6 supports both external and internal oscillators. The OSC_IN and OSC_OUT pins should be crossed to create an external A pair of load capacitors should also be connected to these pins and grounded to improve stability.

5. Programming: For programming, the STM32F429IGT6 supports JTAG and Serial Wire Debug (SWD). For SWD, connect SDIO, WALK, and ground from your programmer to the corresponding pins on the STM32F429IGT6.

6. Peripherals: The STM32F429IGT6 has a wide range of peripherals including SPI, I2C, PART, GPO, etc. Connect these as needed for your application. 

7. Decoupling Capacitors: Place decoupling capacitors close to each VDD pin on the PCB to filter out high-frequency noise on the power supply lines.

8. Voltage Regulator: If your power supply is greater than 3.6V, you will need a voltage regulator to drop the voltage down to an appropriate level for the STM32F429IGT6. 

Please remember, the above guideline is a generic approach and specific needs may vary based on your application requirements. Always consult the data sheet or reference manual for more detailed information.