Should have taken your alternator to get checked. Some places can check it without having to remove it and could have saved yourself some money on that new battery. You're best bet is to get a Helm's manual. Everything you need to know is in there, although replacing an alternator is straight forward. Probably just a few bolts, tensioner and the connector. There's usually between 3-4 long bolts holding it in. Changed the one on my 98 Accord last summer, wasn't difficult. While you're there might as well change the belt too.