I think you need a new battery, and that *should* fix it. I suppose there could be a hardware problem with the computer or charger itself, but it's probably the battery. Which cost about $100 each. You can search online for laptop batteries for that particular laptop. Here's a link to start you off: http://www.laptopbatteries.com/laptop-ba...
I don't know how reliable that site is (never used it) but if you can find something on newegg.com, amazon.com, tigerdirect.com that should be reliable. Even ebay may have a battery. You may also be able to get one directly from Acer.
If the laptop was bought last October, it should still be under warranty (most laptops come with a 1 year warranty). Just call Acer and tell them your problem.
And in the future, get MacBooks. Apple products are very hardy and reliable, and they are simple to use, especially for people who don't already know much about computers. Even other companies like Dell or Compaq should be higher quality than Acer, from what I hear.