Russ,

What you should do is borrow or buy a multi-meter. These are not expensive and very helpful to have ... as in this situation. With the ingnition off connect the (Red)positive lead from the meter to the postive battery terminal. The (Black)negative meter lead to the battery's negative post. Now set the meter to DC volts. The battery should have 12 volts or more with the engine off. Start the engine and the voltage should rise to 13.8 to 14.8 volts. If it's less than 13.8 the battery isn't getting enough juice to charge. The problem could be the
alternator, voltage regulator or wiring. Shut down and now connect the red meter lead to the B+ terminal on the back of the alternator. B+ is where the thick red wire connects to the back of the alternator. Connect the negative meter lead to ground ... the engine ground braided wire or an unpainted bolt head in the engine bay will do. Start the engine and read the voltage ... if it's 13.8-14.8 volts the alternator is good but you have a problem in the wiring ... the voltage isn't getting to the battery. If the voltage is still low or non existant at the back of the alternator the problems is in the alt. It may well be a bad volatge regulator/brush assembly. That can be fixed by simply replacing the VR/Brushes for about 24 bucks for an aftermarket Hugo VR from fcpgroton.come. You aren't necessarily looking at a 200 buck alternator replacement. Because the battery was recently replaced I suspect the battery cables/clamps may be at fault. Having a meter will help you isolate and identify the problem. Well worth the cost of the meter to be able to resolve a lot of these electrical problems yourself. Hope this helps, Good Luck.