How many watts for a PSU do I need?

What CPU are you running?
How much RAM do you currently have?
How many Hard Drives/Solid State Drives do you have?
How many Optical (CD/DVD/BluRay) Drives do you have?
Do you know the brand name of the PSU that you have?

Hmmm... Probably not, but itll be close.

Is it even standard ATX?

PCI Express® based PC is required with one X16 lane graphics slot available on the motherboard
500 Watt or greater power supply with two 75W 6-pin PCI Express® power connectors recommended (600 Watt and four 6-pin connectors for AMD CrossFireX™ technology in dual mode)
Certified power supplies are recommended. Refer to http://ati.amd.com/certifiedPSU for a list of Certified products
Minimum 1GB of system memory
Installation software requires CD-ROM drive, a keyboard, a mouse, and a display
DVD playback requires DVD drive and a DVD
Blu-ray™ playback requires Blu-ray drive and a Blu-ray disc
For an AMD CrossFireX™ system, a second AMD Radeon™ HD 6800 Series Graphics card, an AMD CrossFireX™ Ready motherboard and one AMD CrossFireX™ Bridge Interconnect cable is required
Copied directly from http://www.amd.com/us/products/desktop/graphics/amd-rad...

Also newegg says Minimum of a 650 Watt power supply on the 2GB model from http://www.newegg.com/Product/Product.aspx?Item=N82E168...

In short you will need a stronger PSU even for the 1GB model of the AMD HD Radeon 6870 video card

6870 in an overclocked water cooled I7 / X58 , a more power hungry system than your XPS420
http://www.guru3d.com/article/msi-radeon-6870-hawk-revi...
290 watts from the wall running a game like application
~90% efficient psu
~260 watt DC load
You could run it

Don't want to chance it ?
Any decent 500w with 2x 6 pin connectors
http://www.newegg.com/Product/Product.aspx?Item=N82E168...

are dell PSUs proprietary? or will he be able to switch it out?

If it was I wouldn't have made the reccomendation that I did.