UPDATE: As of Vita firmware Ver. 2.00, the browser is now a "tiny app", meaning it can be run alongside game software without quitting (or having to do the Twitter workaround).
Original answer follows:
While the Web Browser isn't directly accessible while running a game (Vita, PSP or PSOne), there is a workaround to surf to websites while using software.
What you need to do is install the LiveTweet app from the PSN store (available for free). This app is accessible while running games. Either enter your twitter credentials and look for a tweet with a link or use the link to authorize the app that's available if no account is entered, clicking the link will open the web browser w/o closing your currently running game and you can browse to whatever guide or eBook you need, please note that minimizing the browser (using the PS button) will require you to enter it again via the Twitter app. Open webpages will need to be reloaded, so make sure you have internet access when you use this method.
Here's a nice video guide on this workaround:
Another semi-awkward method to use guides while playing games is saving the guides as images and loading them to the picture app, this is actually a bit more convenient if you need to move quickly between the game and guide because you can do so without using other software in the middle, but you'll lose the convenience of searching through the text. You can either use the Vita browser and take screenshots (PS+Start) or use a Chrome extension like Webpage Screenshot and transfer the files over to your Vita.