How do I separate hydraulic disc brake pads after pulling the brake while the wheel is off?

I found this video to be extremely helpful in understanding the problem and solving it:

I fixed my similar situation by removing my disc brake pads and pushing against the pistons behind them with a flat head screw driver. Using a credit card (or similar) to push against the pads wasn't enough for me.

I just had to look this up for a friend, who accidentally completely closed them.

The recommended way, taken from "Zinn and the art of Mountain Bike Maintenance" is as follows. "Sometimes the pads in hydraulic disc brakes can rub because the pistons get pushed out too far, especially if the lever is applied without a rotor or spacer between the pads. You will have to push the pistons back in, usually by removing the pads and pushing the pistons back in with a plastic tire lever. On Hayes, the only thing pulling the pistons back in is the reversal of the twist the pistons apply to square-cross-section o-ring seals surrounding the waist of each piston, so the pistons tend to stay out too far once there. Pull out the pads, carefully push the pistons back in with the box end of a 10mm wrench(avoid pressing on the pin sticking out of the piston, which hooks the wire catch on the back of the pad), and replace the pad"

Not as practical as some of the other solutions, but if you know a car guy, they've probably got brake pad spreaders laying around. You should be able to get an edge or corner far enough in to use them.

As mentioned try a blunt bladed instrument (A large flat blade screwdriver will do) to pry the pads back in. Just put the screwdriver between the pads and lever the pads apart evenly! Just be carful though as sometimes the pistons that push the pads out can come out too far resulting in the pistons being slighly out of line, however if the pads have plenty of material left on them you should be fine to just lever them back in with the screwdriver, ther will be some resistance as you will also be pushing against the pistons and fluid pressure.

I've used a (clean) drywall putty knife. The blade is wider than a screwdriver, so there's less chance of gouging the pads. Slide the knife in between the pads, twist and pry a bit, and they open right up.

You could try blowing them with air to remove any dust particle that may prevent them for separating completely. If that's not enough you can use a "flat" screwdriver. When you have the screwdriver between the pads turn it carefully not to damage the brake pads and separate them a little bit.