Will buying and installing a new power supply for a Dell 4600 say to 350 or 400 watt be as simple as doing it? Or do I have to consider the motherboard and other circuits with the increase wattage?
Well installing part is really that easy you just tighten a few screws and plug in some cables. Cables are foolproof so you can't plug them to a wrong socket.
You do need to consider all of the parts of your pc including external devices and stuff but a 400W PSU will be enough for an average PC. If you have a high end GPU then you might want to calculate how much you really need.
I guess being more specific would help. Right now I have a 250 watt psu and in order to install a new graphics card that has a 300+ wattage rating I would need the extra wattage. The other parts of my pc would use what they needed and not be fried by the excess wattage right? That is my assumption about wattage but voltage would be another story right?
Your assumption about wattage is correct. Your system could be drawing something like 180W total right now. If you put in a 700W power supply, it will still only draw 180W.
Wattage is voltage multiplied by current. Each part will only draw as much current as it needs. The voltage will be constant, which is why you plug the parts that run on +12V into +12V on the power supply.
I believe the wattage rating takes into account an "average system" and ads that. I know that even the radeon 5870 only draws up to 188W on its own. You'll definitely need a new power supply, and 400W will probably be enough or 500W to be safe, but if you give us your system specs and replacement video card, we can tell you how much you'll need.
I think with yours and others help I'm zeroing in on my problem. As I mentioned earlier with the 250 watt PSU I'm running a GeForce 6200 256 mb rated for a minimum 300 watts. With this setup everything was running fine with XP on my system but back in October I went to Windows 7 and thats when I started having problems. When running Outlook 2007 with nothing else open I get a flickering screen accompanied with "not responding" messages. This is especially true when trying to select an attachment to send. Its a never ending flickering session until I can get task manager to finally shut it down. I have reinstalled Outlook, repaired Outlook and nothing seems to help. I have the latest drivers from Nvidia and that hasn't helped. I don't know much about Windows Aero but I have a feeling this might be part of the problem. I think I'll just jump on up to around 500 watts if I can find a unit that will fit into my Dell 4600. By the way I have 4 gb of ram so I don't think that could be a contributing factor.