The Nintendo DS Lite cannot browse the modern web. It lacks a built-in browser, modern Wi-Fi hardware, and the processing power needed for contemporary websites.
Nintendo released the Nintendo DS Browser (a cartridge plus RAM expansion pack) in 2006–2007. It used the Opera engine but was extremely limited:
The DS Lite's Wi-Fi was designed for Nintendo Wi-Fi Connection (discontinued 2014) for multiplayer in games like Mario Kart DS, Pokémon Diamond/Pearl, Animal Crossing: Wild World. Community projects like Wiimmfi restore online play for supported titles using custom DNS settings.
Bottom line: For web browsing, use a smartphone. For DS online gaming, explore Wiimmfi with a flashcart or DSi/3DS.