What kind of computer is it? If it's a name brand and you know the model name/number that would help... or if you know the model number of your motherboard. Other than that, pull the case cover off and look inside.
Considering it's new I'd imagine it has PCI-Express x16... that's what you want anyway.
Here's what they look like
From top to bottom:
PCI-E x4
PCI-E x16
PCI-E x1
PCI-E x16
PCI
If it's AGP, the AGP slot will be offset further back than the standard PCI's, like this (this pic also shows you the motherboard brand, ABIT, and the model number, BE6-II)
