I own an HP Pavilion a1310N which has the video card located on the mother board. Is there any way I can use an external card for better graphics? I don't mind adding an extra power supply if that is necessary.
According to this, you have an available PCI-Ex16 graphics card slot. Which graphic card you should get is going to depend on a couple things:
1) What processor is currently installed? - It looks like the base model comes with a single core AMD s939 3700+. If this is the case with your system, then you probably don't want to put an overly powerful graphics card in there. Additionally, since it is an older system (socket 939 systems are functional, but defunct these days) I'm betting it follows a PCI-E 1.0 standard which means graphic cards that follow PCI-E 2.1 standards may cause issues (PCI-E 2.0 cards are fine though).
2) A more powerful graphics card will likely require a more powerful power supply. It's not a matter of adding a secondary power supply as it is replacing your current power supply. What new power supply wattage you need (if any) is going to depend your budget for these upgrades and what graphics card you select.
So if you could provide us with your current system specifications (CPU, Power Supply, RAM) we can make a decent suggestion for you.