How to run phone with power supply?

I'd suggest going with a pre-made adapter, myself. They're cheap and easy to get; here's one that would work fine for about $4 USD.

iPhone battery wire adapter cable for DC power supply

But to answer your question, here's a diagram of the battery connector on the motherboard from repair.wiki.

Pins 1 and 5 are positive and all the green ones, pins 4 and 6 in particular, are negative (ground). Pins 2 and 3 are for the phone to communicate with the battery. Note that you will most likely run into a 3 minute boot loop without the BMS being connected.