You could wait, and wait, and wait for Sony to release V2 firmware for the PSP so you could browse the web. You could also royally screw up your PSP by trying to load Japanese V2 firmware. OR, you could simply follow the link below to grab the 1.5 (works on 1.5 only) web browser for PSP which will work on your US system, if you don't mind pressing the select button to switch the language from Chinese to English.
(FYI, try this only if you are confident with what you are doing. We're not condoning this unofficial software, just reporting it.)
Underground Web-Browser released for the PSP v1.5.