Microcontroller Interface with Modbus Serial
There are a number of questions you need to answer before connecting to a Modbus interface:

1) What is the physical layer?

Modbus can be transported over a RS-232, RS-485, or Ethernet. Based on your question I'm going to assume you've already determined that it is RS-232.

2) What are the parameters of the RS-232 connection?

You will need to know baud rate, data bits, stop bits, parity, and whether or not there is any flow control being used.

Typically baud rate varies from controller to controller, but the remaining parameters will almost certainly be 8 data bits, 1 stop bit, no parity, and no flow control.

3) What are the parameters of the Modbus connection?

In order to communicate with a Modbus device you must first know what format of Modbus is being used this will be ASCII or RTU. ASCII you could in theory use a terminal program and manually type in the requests and receive responses. RTU you will need to write software to send command/response bytes between LabView and the micro controller. For either format you will need the drop number of the device you are communicating with since sometimes multiple Modbus devices will exist on a single network.

4) You will need software that can form and send Modbus request packets 
and receive and parse the Modbus response packets. 

For more details on what these packets look like refer to the Modbus specification under technical information at Modbus.org. If you want to test that the Modbus communication is working I'd recommend a program such as ModScan. Once you've verified that the Modbus communication between the PC and the device is working you can take on the next step of interfacing LabView with Modbus.