connect my pc to lcd tv hdmi

i use the exact same set-up at home.
1. most TVs (LCD) will have a VGA in. so you can connect the VGA(15 pin ) out directly to the TV.
2. it is pretty clear. if the TV is hdtv, you can use the max supported resolution (1920x768) or 1920x1080. i use a wireless kbd and mouse and it works perfect. let  me know if you have questions on this.
3. if the TV comes with a 3.5 mm socket for audio input corresponding VGA video input, you can connect it directly from teh speaker out from the computer. otherwise you will need a cable 3.5mm - stereo RCA to connect to the audio terminal on teh TV.  if you are using an audio receiver,  you most probably will need the 3.5mm to RCA cable.
--Gopa

DVI to HDMI will be very clear, as good as the output on the computer can produce.  I have set up a number of HTPCs in my day and this always produces results that are pretty good for video and gaming.  The issue comes in that the output of a computer is not designed for a large formats and you may find that doing other work, and looking at the desktop, it may not be what you expect.

I am wanting to take a desktop pc and connect it to my 42 inch LCD hi def tv and use it for things like browsing the internet and watching my dvd movies.  a couple of questions.

1. do i need to find a video card with a HDMI output? If  so can someone recommend one.
-I would most certainly not use an HDMI video card. Most of these are expensive, and do not give you any more of a better picture then dvi - hdmi cable. I myself am an Newegg and Nvidia fan and will reccomend anything with the 8000 series or better. ( http://www.newegg.com/Product/Product.aspx?Item=N82E16814130338 )

2. how clear will it be? I am hoping I can use a wireless keyboard and mouse to sit on my couch and browse the internet.
-It will be as clear as your current monitor as long as you use the base resolution. You will be happy with the usage in my opinion.

3. what problems will i encounter? what do i do about audio?
-There is going to be very little problems provided you know how to set it up and you know what you are doing. Does your TV have a DVI hookup? Does it have digital audio input? How are your plans to hook up the audio? You can use digital audio out from the pc with a good quality sound card and input on your TV. You can also have rca outputs from the computer to the TV.

-Todd Beedy

Brank20 is correct
you will get many opinions here but I do this everyday for a living.

theoretically you will get the best image you can ever get using HDMI or DVI-D because these are digital signals, no signal loss occurs.  You either get the image or you don't.  

using analog or 15HD(VGA) or component you can get a good image also but this requires the display be set up properly, use of a low loss cable, etc.  With analog the quality can vary.  You must be sure to output the native resolution of the LCD from your computer.  If you do not, the image will not look very good because the LCD will be using its internal circuitry to change the incoming image to its native resolution.  This means it will try to either remove video information or add video information, neither of which are good.

HDMI and DVI-D are the same except:
HDMI carries  HDCP content protection keys, Audio, Video
DVI-D carries  video

this means if you use a DVI-D card on your computer then you will need to also transmit audio from your 3.5mm port on your computer and you will not be able to view content protected material, like protected DVD's from your computer.  you can use a DVI to HDMI adapter to use HDMI cable and get a longer cable run.

If you get HDMI on your computer, you can use a longer cable, you can support content protection(just make sure the card says it will support HDCP).

DVI-I is analog and digital on same connector
DVI-D is digital only, anything that DVI-D will do, DVI-I will do also.
DVI-A is analog only