The STM32F437IIT6 is a 32-bit microcontroller based on the ARM Cortex-M4F core from Microelectronics. It features 2048 KB of flash memory, 256 KB of SRAM, and it operates at a frequency of up to 180MHz. Here's a simplified guide on how to connect the STM32F437IIT6 microcontroller:

1. Power Supply: Pins VDD (Pins 11, 19, 32, 49, 64, 78, 90, 103 on LQFP176 package) should be connected to a 3.3V power supply. The VSS pins (Pins 12, 20, 31, 48, 63, 77, 91, 104 on LQFP176 package) are ground pins and should be connected to the ground of your system.

2. I/O Pins: The STM32F437IIT6 has multiple I/O pins that can be configured in various modes such as GPO, ADC, DAC, I2C, SPI, SART, etc. Connect these pins according to your application requirements.

3. Reset: The NRST pin (Pin 7 on LQFP176 package) is a reset pin. Connect a push button to this pin and ground to create a manual reset. Alternatively, this pin can be connected to an external microcontroller for software control of the reset.

4. Boot Mode: The BOOT0 and BOOT1 (Pins 138 and 37 on LQFP176 package) pins are used to select the boot source. Connect these pins to either VDD or VSS depending on your boot requirements.

5. Oscillator: The HSE (Pins 9 and 10 on LQFP176 package) and LSE (Pins 42 and 43 on LQFP176 package) pins are for connecting an external oscillator if required by your application. The HSE oscillator frequency range is from 4 to 26 MHz, the LSE is from 32.768 kHz.

6. Debugging: The SDIO and SWCLK pins (Pins 34 and 37 on LQFP176 package) are for connecting to the ST-LINK/V2 for programming and debugging the microcontroller.

Please note, this is a very simplified guide and the actual connections can be more complex depending on the specific use case. Always refer to the data sheet and reference manual of the STM32F437IIT6 for detailed information and follow the recommended practices for PCB layout and design. The STM32F437IIT6 is a highly versatile microcontroller and supports a wide variety of peripherals and interfaces.