I've heard conflicting reports about whether Dell ships stock PSUs or forces special/proprietary PSUs.
Dell ships at least some of their computers with proprietary PSUs.
There are a few website which sell PSU models with specific mention to be compatible with a specific Dell model. Google them. (I am not going to link to a specific one).
How exactly can I determine if a PSU is compatible with my PC, before buying it?
Ask the seller to guarantee that it will work with your model. If you phone them explicitly tell them about the model you have. Or use a webshop which sells models specifically for Dells.
I assume I will not be able to return it if it doesn't fit,
Why not? Law differs per country, but most places allow you to return an undamaged, unscratched unit, with all original parts (e.g. box) still present.
or makes my computer explode in a fireball of doom.
This is actually possible since the pin-outs on some Dell PSU's are different from normal PSU.
Also, you did nt ask this but I see this a lot on the web:
a AMD HD6770 which demands at least 450W
Uhm. No. Not precisely.
Graphics cards do not demand PSU of at least XXX power. That is just how shops sell it. They do demand a certain amperage on the 12 volt rails, and depending on the card they use 6 or 8 pin connectors.
If you have a big lot-of-watts PSU then it often also supplies enough power on +12. But that is not guaranteed. You really want to check how much the PSU outputs on different rails and how much your graphics card needs. Not how much the PSU can supply in total.