The focus here is on the ATSAM3X8EA-AU, an ARM Cortex-M3 based microcontroller (MCU) from Microchip. Its versatility comes with an array of features including flash memory, analog-to-digital converters, and multiple connectivity options. Now, let's dive into the detail on how to connect this MCU properly.

1. Power Supply:The RADIO (pins 8, 46, 75, 96, and 144) is for the I/O supply voltage and VD DIN (pins 45 and 96) is for the internal regulator input. A 3.3V power source needs to be attached to these pins. The GND (pins 9, 47, 76, 97, and 145) should be connected to the ground.

2. Crystal Oscillator:The XOUT32 (pin 19) and XIN32 (pin 20) connect to a crystal oscillator operating at 32.768 kHz. This provides a clock source for the RTC and can also be used for general system clocking.

3. Analog-to-Digital Converter (ADC):ADC inputs are provided on pins 93-100 (AD0-AD7). If your application requires an ADC, one of these pins would be connected to your analog signal, with the reference voltage applied to the ADORED (pin 92).

4. Connectivity:This MCU has multiple options for connectivity, including PART, SPI, I2C, and CAN. For example, UART0 uses RXD0 (pin 141) and TXD0 (pin 142), SPI uses MISS (pin 108), MOST (pin 109), SICK (pin 110), and NPCS0 (pin 111).

5. Reset: To externally reset the MCU, utilize the NRST (pin 152). This pin should be connected to a reset button that pulls the pin low when pressed.

The connection methods for the ATSAM3X8EA-AU MCU are numerous and depend on the specific needs of your application. It is critical to always refer to the ATSAM3X8EA-AU data sheet and understand the functions of all the pins and peripherals in detail. Note that in any real-world application, it's crucial to design for power decoupling, signal integrity, and ESD protection. These aspects are not covered in this high-level guide, but are necessary for the proper operation and reliability of the ATSAM3X8EA-AU MCU.