When your alternator starts to go, it makes an audible low "wheeeeeeeeeee" sound. Turn off your radio and fans and listen while its running.
You can test with a device -I don't remember it's name, but it's a simple meter with two clamps that reads the voltage going to your battery.
A rebuilt alternator like Champion is pretty cheap, well under $200, and it's an easy job to replace. You can get the brushes and bearings replaced for about $40. A wrecker's alternator should be under $20.