In the "How to Capture Packets with Tshark" YouTube video, the speaker shows how to use Tshark, a command-line tool within Wireshark, to capture network packets. To start, the user opens the command prompt as an administrator and navigates to the Wireshark installation directory. The speaker explains using switches to list interfaces, select one for capturing, save the capture to a pcap file, and avoid promiscuous mode. The speaker captures the first 100 packets and demonstrates viewing them using Tshark's command-line interface, displaying details like unique packet numbers, IP addresses, domain names, and protocol information.