Firebug plugin for Firefox has always been a popular choice, but most browsers now provide similar debugging capabilities, personally I still tend to use Firebug, you can set breakpoints and step through your code, that sort of thing.
Be warned though when using App Editor, it always reloads files from the server each time you "save and run" so any breakpoints previously set wont work. So if you are going to use a debugger to step through your app code and you need to set breakpoints before teh app loads you'll need to run it in a seperate browser window and make sure you clear your browser cache each time you make changes.
The console methods, such as console.log, error, warn etc, are all still popular too, and now supported by most browsers (equivalent of System.out.println).
I am new to presto and really open source tools and languages in general. What is the best/easiest way to set breakpoints and generalyl debug custom apps? I'm using Eclipse for the mashups, which works ok, but I can't figure out how to use that for apps created with the app editor, and the app editor is not very helpful for debugging. What do most people use?