For all the journey maps that we create, we export to images and then if you want to share them, put them into presentations. So we've used omnigraffle, or even illustrator etc to make them in the first place. But if you want to make more creative journey maps, you could even try what Matt and Luke did with recording sketch stories (see an example here https://www.youtube.com/watch?v=Ovj4hFxko7c).
For recording user experience with real websites:
You can either do this in an informative or summative way. So for informative, you might for instance do in-person testing, where you set someone tasks to complete, and then you record the screen with a screen capture program. You would also write notes down as they go.
For summative google analytics can be good for some, but you really need to back them up with what you got from the informative studies, as they don't really tell you why things happened, just that something seems to be occurring.
I personally believe that if you want to show analytics etc to non-digital stakeholders you need to make it interesting and look nice, not just a whole lot of statistics and bullet points. So either having short video clips, highlighting main points, or nice infographics with what you found out can be a good start. Something more along the lines of the sketch story may be a lot more interesting than an image on a piece of paper, but it really does depend on your audience type as well.
Does anyone else on here have experience using good software for analytics testing of websites?