To connect your computer or mobile device to the HP DeskJet 2621 printer, follow these steps. For a computer, ensure it's on the same Wi-Fi network as the printer. Install the necessary drivers by visiting the HP website or using the included installation CD. Then click 'Print' while the document is open. Choose the DeskJet 2621 from the list of available printers. If connecting a mobile device, download the HP Smart app from the respective app store.