In my boat, the trolling batteries, charger or both are not working correctly (the charger shows power only on one of the two banks, but the battery does not charge or progress to the 'green' indicator). I can have the batteries tested easily enough, but can someone tell me if there is a fairly simple way to test the charger to see if its putting out the power that it should?

I'd imagine a voltmeter would work, but does anyone have experience with this that they could help me out with?

Thanks

You are right, just use a voltmeter on the one of the charger's bank outputs.  My charger ramps up to 14.6 volts during the charging stage, holds steady at 14.6V during the conditioning stage, and then drops down to 13.3V when it enters the maintenance/float stage.

I had a similar problem a few years ago and it turned out the batteries were kaput.

You should have fuses or fusible links near the batteries. Check those out before you condemn the charger or the batteries. If those are ok check the output of the charger with a dc voltmeter