Monitor + HDMI to TV question?

I'm hoping someone can help me out here.  I'm coming into possession of an Inspiron 580 that was going t o a family member.  I've been working off a laptop for the past 8 years so i really don't know much about desktop setups.

I've had my laptop connected to my tv through an HDMI cable, will I be able to continue doing this with the 580?  I'm just not sure where the desktops monitor plugs into, if it's the same place where I would plug in the tv so I can only have one at a time or if it is two different spots and I can have both plugged in at once.