A versatile 8/16-bit AVR microcontroller from Microchip, the ATXMEGA128A4U-AU has a number of inbuilt peripherals for a variety of applications. Here are steps on how to connect the ATXMEGA128A4U-AU in your circuit:

1. Power Supply: The ATXMEGA128A4U-AU operates between 1.6V to 3.6V, which should be connected to the VCC and GND pins. It's recommended to use decoupling capacitors close to these pins to minimize power supply noise. An optional separate analog supply (ACC and AND) can be used for the ADC and DAC, to reduce digital noise.

2. Clock Source: This microcontroller can operate using an internal RC oscillator, an external crystal, or an external clock source.The XTAL1 and XTAL2 pins must be connected if an external crystal is being used.

3. Push-button switch connection for manual resetting: Attach a pushbutton switch to the RESET pin. The RESET pin is active low and includes an internal pull-up resistor, but an external pull-up resistor can be added for additional noise immunity.

4. JTAG Interface: For programming and debugging, connect a JTAG programmer/debugger to the TMS, TCK, TO, TDI, and RESET pins. Alternatively, PDI (Program and Debug Interface) programming can be used, which requires only the PDI_DATA and PDI_CLK pins.

5. Peripheral Connections: The ATXMEGA128A4U-AU includes multiple communication interfaces like PART, SPI, I2C, and USB. Connect these according to your system needs. For ADC and DAC applications, ensure proper signal conditioning for the input signals.

6. GPO: There are multiple General Purpose I/O pins available. These can be configured in software as input or output, and can be used to interface with LEDs, switches, and other digital devices.

7. External Interrupts: If you need to use external interrupts, connect the triggering signals to the appropriate Port interrupt pins.

Remember, the above steps provide a high-level view and actual implementation might require additional considerations for signal conditioning, interfacing, power management, and PCB layout. Always refer to the ATXMEGA128A4U-AU data sheet and relevant application notes for detailed information and guidelines.