To connect your HP DeskJet 4100 printer to Wi-Fi, press and hold the Wi-Fi button and the Cancel button on the printer simultaneously for about 3 seconds until the Wi-Fi light starts flashing. Then, use the HP Smart app on your phone or computer to add the printer and connect it to your Wi-Fi network by selecting your network and entering the password.

Here are the detailed steps based on the latest guidance:

1. On the printer, press and hold the Wi-Fi button and the Cancel button together for 3 seconds until the Wi-Fi indicator flashes.
2. Download and open the HP Smart app on your smartphone or computer.
3. In the app, add a new printer by selecting the plus (+) sign and choosing your HP DeskJet 4100 from the list.
4. Follow the on-screen prompts to select your Wi-Fi network and enter the password (usually found on your router if you don’t know it).
5. The printer will connect to your Wi-Fi network and be ready for wireless printing.

Alternative connection methods include:
– Using WPS (Wi-Fi Protected Setup) if your router supports it — press the WPS button on the router and then the Wi-Fi button on the printer to connect automatically.
– Connecting via Wi-Fi Direct to print without a network.

Sources:
– [HP Deskjet 4100 wireless setup video, March 2024](https://www.youtube.com/watch?v=zta3fIshG5o)
– [Step-by-step Wi-Fi connection methods video, Sept 2024](https://www.youtube.com/watch?v=6tWJNl8DTbo)
– [HP support community instructions, May 2024](https://h30434.www3.hp.com/t5/Printer-Wireless-Networking-Internet/How-to-change-the-WIFI-network-on-my-HP4100-printer/td-p/9075761)