The old browser trick basically had you open a web browser, go to the market in the browser, and search for google wallet. Then install it on your Galaxy Nexus. How to: Install Google Wallet From the Market on the Verizon LTE Galaxy Nexus – Droid Life <-- with instructions and video. That is from Feb, so it is old and probably outdated/non-working by now.
https://play.google.com/store/apps/d...etgooglewallet <-- that seems to get good reviews. Seems to be VZW GN users using it, so perhaps it works.
To update ROM you download it, and Gapps if required, and install them in custom recvoery. It may require a wipe if coming from a different ROM or the developer recommends it.