How do i connect HDMI up?

You'll need a DVI to HDMI adapter. In other words, your connection will look like this:

Native DVI out on 8800 GTS - DVI to HDMI adapter - HDMI cable - HDMI in on monitor

Possible follow up questions:

What's a DVI port look like?
Do an image search on your search engine of choice. I'm sure you will get results.

Where do I get a DVI to HDMI adapter?
They are quite common. Many modern graphics cards are even bundled with them. If your card wasn't, try newegg, but don't pay more than $7 - 8 for one.

If i use an adapter will i lose any picture quality if i am not running a movie or game in HD?

I had this question a few months ago and was told that an adapter would not result in a loss of picture quality.

However, I was never given a technical response and as a result, am not completely satisfied with that answer. In fact, I kinda hope someone else chimes in on this thread with a more insightful answer.

I will say this though, one of the major differences between HDMI and DVI is that HDMI cables can carry both sound and video over, while DVI is limited to only video. As a result, one of the advanatges of a native HDMI port coupled with a graphics card with onboard sound, AKA ATI's HD 4000 series, is that its allows its user to experience sound and video with less cable work.

I might add... I too am using a DVI/HDMI adaptor. It woks great, no loss of quality. Just check that (if you're using a HDTV) one of your HDMI ports may be specifically designed for computer use as opposed to the others. Overscan and poor quality picture may result with using the wrong HDMI port. That's the way my Samsung 32" was.

DVI-HDMI send the same exact video signal; no loss of quality occurs.