Wow... small world. I just went through this over the weekend with my '06.
Watch this guy's video:

extremely helpful demo of how to do this and he mentions that spill-proof funnel, although he shows you how to do it with a regular funnel and duct tape (which is what I did). This car is notoriously difficult to "burp" the air out of. In answer to your questions:

1. Definitely have to start with a cold engine, overflow reservoir no more than half full, remove the radiator cap, put in as much coolant as the radiator will hold. Then you put that funnel thing into the radiator, or a regular funnel with duct tape wrapped around its spout so it fits tightly into the radiator opening. Pour some coolant into the funnel. It must be enough to just come up in the bottom of the funnel, but no more than 1/4 of the way up. It HAS to fit tightly or coolant will ooze up out of the radiator opening and drip/leak all over the place. And you don't want to fill it more than 1/4 of the way because as the radiator water expands, it might climb up and over the sides of the funnel if you start out with it too full.

2. Start the engine, turn the heater on. On the 1st gen Murano, this means setting the temp to something like 90, manually turn OFF the A/C.

3. As the engine runs, you will see air burp up out of the funnel, and the level drop. As it does, keep adding coolant to keep a little in the funnel. Every time it burps out air, you want some coolant to drop in to replace it.

This has to go on until the thermostat opens, at which point you may see a rapid drop in the funnel level, just keep adding coolant to keep up with it. Rev the engine up to 2000 rpm for about 20 seconds every couple of minutes. That will force coolant through the engine and heater core more rapidly, which will chase air bubbles out through the funnel.

PATIENCE is key. The engine needs to run about 20 minutes, long enough for your radiator fans to go on and off at least twice. The guy in that video mentions it, but it is ESSENTIAL to wait for several fan cycles. Feel the vents for heat. Until you start getting hot air blowing, you're not done.
In my case, it took more like 30 minutes before all the air burped out and I was getting solid heat. I thought I was done until the fans kicked on the first time and the coolant level in the funnel dropped dramatically.

 

Thanks to that video and the annotations, I just edited the thread title slightly and made it a sticky.

 

You probably have an air pocket in the system. If you have an incline to park on, park facing uphill with the engine running and the radiator cap removed. It should burp out the air, add coolant to top off.

Or, what I use is a Lisle funnel, it accomplishes the same thing, but also works on a level surface.

Amazon.com: Lisle 24680 Spill-Free Funnel, Standard Adapters, 11 x 7 x 7 inches : Everything Else

 

I'll definitely try that! How long should I leave the car running, and should I take the radiator cap off before I start the car?

 

Excellent instructions.

I think one of the key things is to wait long enough for the thermostat to open to allow all the air in the system to exit out of the radiator cap opening.