For starters, if you don't get service at all, you definitely want to consider powering your phone off or turning off the service. You can change that by going to "Manage Connections" or whatever it's called. Otherwise your phone will be searching for a network the entire time, which will easily drain your battery life.
Secondly, you're going to want to make sure you have as few (preferrably none) applications running in the background as possible. You said yourself that you leave the browser running all the time, but keep in mind that just because it's not on the screen doesn't mean it's not running and using battery life in the background. You want to use Menu->Exit/Close or the Escape button (arrow) to exit completely out of programs to make sure they're not running in the background.
You can hit ALT+ESCAPE (while holding alt) to cycle through all the applications currently running. There should only be 5 in that list (you can check the FAQ for more details on this), but anything else is programs running in the background, and depending on the application, it can be a minor or major impact on your battery life.