Still not sure what your question is about... The tag "arduino" let me think you are asking about Arduino code, but the comment below make me doubt you are asking for .NET stuff. Here's a tentative answer should the question be on how to manage things on the Arduino side.
Method 1: using serial communication and a proxy
On the Arduino, I would simply output SQL queries on the Serial port, like this:
Serial.begin(115200);
Serial.println("INSERT INTO table_name VALUES (value1, value2, value3,...);");
On the server side (or on the side of the computer you are using to access the Internet), I would write a simple script that opens the connection with the DB and forward the query to it. This could be achieved either by CLI commands or opening a network connection on a given port. I do not use Windows/.NET, etc... but on a GNU/Linux box, using python and mysql, the proof-of-concept code that I would write would look something like (BEWARE: UNTESTED!):
import os, serial
self.ser = serial.Serial("/dev/ttyUSB0", 115200)
query = self.ser.readline().strip()
return os.popen("mysql -u<my_usr> -hlocalhost -p<my_pass> -e" + query)
Method 2: using a lan shield or directly an Arduino LAN board
The latter will be shipped sometimes soon (see this presentation if you are curious about it). The first is already available. Writing the code for it should be dead easy (see docs here). The result should be something down the line of (UNTESTED):
Serial.begin(<speed>);
Ethernet.begin(<mac_number>, <ip>);
Client client(<server>, <port>);
client.println("GET <path> HTTP/1.0");
while (client.available()) {
char c = client.read();
Serial.print(c);
}
HTH!