Where does a graphics card go in a Windows vista 7, Acer home premium?

We can't really say unless you give us the specific model number of your PC.

What do you mean you opened your monitor?

From post # 1

I opened my monitor today to see where will a graphics card go

Please complete this tutorial by Brink.

System Info - See Your System Specs

My guess is that you are talking about an Acer all-in-one desktop. It's usually not possible to change the graphics card in such a computer but as has been requested, can you provide us the exact model number? With the exact model number someone can give you the correct information.

Page 70 of your manual shows two PCIe slots, one x1, one x16.
http://tim.id.au/laptops/acer/aspire...%20asx3200.pdf
Googling this issue shows that you would need a half-height ("low profile") video card, not a standard one.
Your case is too narrow for a standard video card.
Page 5 shows a card installed in the upper right corner of the motherboard.
Reports also say that if you're going to add a graphics card, you usually need to upgrade your power supply. This is just about impossible, because the Acer PSU seems to be proprietary and physically small, meaning you can't just install a bigger standard PSU from off the shelf. The only one that will fit is another Acer 220 watt model.
You'd also need to probably add a fan somewhere, because graphics cards can pump out a lot of heat. In that tight case, a card could overheat really fast unless you address cooling.

This is not a "Gaming" PC. Max memory, listed in the tech specs is only 2GB. The 220 watt power supply MAY be (and its a big MAYBE) a BTX, and if that is the case it can be upgraded, but I haven't seen any high power BTX power supplies.

If the 2GB RAM max is true there is also no need for the 64 bit OS.

Iov said:

OvenMaster said:

Page 70 of your manual shows two PCIe slots, one x1, one x16.
http://tim.id.au/laptops/acer/aspire...%20asx3200.pdf
Googling this issue shows that you would need a half-height ("low profile") video card, not a standard one.
Your case is too narrow for a standard video card.
Page 5 shows a card installed in the upper right corner of the motherboard.
Reports also say that if you're going to add a graphics card, you usually need to upgrade your power supply. This is just about impossible, because the Acer PSU seems to be proprietary and physically small, meaning you can't just install a bigger standard PSU from off the shelf. The only one that will fit is another Acer 220 watt model.
You'd also need to probably add a fan somewhere, because graphics cards can pump out a lot of heat. In that tight case, a card could overheat really fast unless you address cooling.

Sucks. So basically I cant install a graphics card? I was hoping to use the computer for gaming. Is there any cards out there that may be able to fit in my case? And once again in orrder for the card to work, all the slots on the graphics card have to be plugged?

You could install a card, but you'd most likely need a fanless, half-height card that doesn't suck up a lot of juice. Those don't game well at all. And no, you only have to plug the card into ONE slot, usually the larger X16 one.
Fireberd's right. This is no gaming machine. I took another look at the way your case is stuffed full: there's no room for a decent fan. So this means that you're restricted in physical space for a video card, you would have poor airflow in order to cool one, you can't get a more powerful PSU to power a decent video card, and page 85 says you're limited to just 2GB of RAM.

Don't waste your money.