You can run a capture using a sniffer program, for example: Windump) You can then monitor the output stream of the program, or write to a file and later analyze it. Some sniffers let you generate a filter so you only capture Internet data, though. This will depend on the actual sniffer used, so check their documentation.
These CP projects may help you:
A Network Sniffer in C#[
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Internet Traffic Firewall and Sniffer[
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