Your video card has a DVI port , HDMI port and two mini Display ports so you need an adaptor and The card does come with a dvi to vga adaptor. So what you'll have to do is connect the dvi on the card to the monitor with the dvi connection. Then the other monitor that has the vga connection you'll have to get this cable.
I really don't want to buy any adapters unless needed. The 1st monitor is 23" and 1080p and the 2nd monitor is some old emachines monitor. The emachines will be used for Facebook and other non graphic programs. So would I still need an adapter?
Go to the "Advanced" section of the BIOS and then go to "North Bridge Configuration". In that menu, set "IGPU Multi-Monitor" to Enabled.
Your primary display will be the one connected to your GPU (the 1080p monitor, and the one that you will see the BIOS and boot-up with), but the second display (the eMachines monitor and the one connected to your motherboard) should be available once Windows starts.
Edit: You'll need to install the Intel graphics drivers too, when you do that. It should work without doing it, but you should do it anyway.