This process is a little janky and IMO doesn't always work like it should. None the less, here is how I do it...
I should mention that even tho the screenshots show that I'm using a Asus ZenWatch, this process should work with any Android Wear watch / Android phone 4.3 or higher combination.
1) Open Android Wear app, pull down options menu.
2) Go to your Android Wear smartwatch and navigate to the screen you want captured / screenshotted.
3) Quickly go back to your phone and tap the "Take wearable screenshot" option. I say to do this "quickly", because if the watch dims or turns it's screen off you will get a screenshot of that... Not what you wanted.
4a) You should see a notification in your notification shade in a moment that looks like this...
4b) Pull down your notification shade and tap that notification that says, "Wearable screenshot finished".
5)
NOTE: This is usually where things get a little janky and may not work as intended. If you encounter problems, repeat steps 1 - 4 and select a different option below...
You should now receive a pop-up menu asking you to select an app to complete this action with:
I usually use Dropbox (as you can see), but if you have a file explorer installed (I use Solid Explorer) that will work as well. Feel free to experiment and try different apps, just follow the note above if something goes wrong.
For the sake of this example, I'll choose "Solid Explorer"...
6) Solid explorer (or whatever app you chose) will usually ask you where you want that file to be saved, select the appropriate destination folder...
7) For those paying attention, you might notice that you never got to pick a filename. This is because the screenshot is ALWAYS called "screen.png". Look for that file in Solid explorer (or whatever app you used).
That's it... Your done!
Special note... Since the filename is always the same, if you take another screenshot and save it in the same place, you will have an issue that there is already a file by that name (prompting a " do you want to overwrite " message). To avoid this, rename the screenshot each time after you save it.