It took me the longest time to figure this one out too, so you're not alone in being puzzled. I kept looking for a "radar spot" icon (y'know, like the button you push to have it show your current location on the map view) but there isn't one that lets you do that.

Fortunately, when your question came in, I was driving through Oklahoma -- of all things -- and captured a few iPhone screen shots to show you the correct process.

First off, here are the directions I was seeing on my phone:

Pushing the "Edit" button on the top left got me here:

Problem was, I didn't care about the previous starting point, I wanted to know how much time was left in the drive from my current location to my desired destination (scenic Ardmore, Oklahoma).

Here's the secret.

Ready?

Just start typing in current location and...

ta daaa! it shows you the matches as you type, just like any other iPhone app, but in this case the possible match of "current location" is shown in blue to differentiate it from any other option.

Tap on it and ...

Finally, press "Route" in the lower right and you'll indeed update that end point:

So that's the secret and it's not clear at all: just type cu or so and you'll see "current location" pop up as a completion possibility. Choose it and you're golden!