The PSP was never designed for general web browsing. Its internet capabilities are narrow, model-dependent, and largely obsolete today.
Custom firmware (CFW) + homebrew browsers (like Links or Simple Browser) can enable limited web access, but it's complex, risky (brick/ban), voids warranty, and the experience is poor—tiny screen, no keyboard, ancient rendering engine.
Bottom line: For internet, use a smartphone, computer, or tablet. The PSP is for gaming.