How can I run my python script from within a web browser and process the results?
After following the django tutorial, as suggested in a comment above, you'll want to create a view that has a text field and a submit button.  On submission of the form, your view can run the script that you wrote (either imported from another file or copy and pasted; importing is probably preferable if it's complicated, but yours sounds like it's just a few lines), then return the number that you calculated.  If you want to get really fancy, you could do this with some javascript and an ajax request, but if you're just starting, you should do it with a simple form first.
I have a written a short python script which takes a text and does a few things with it. For example it has a function which counts the words in the text and returns the number.
How can I run this script within django?
I want to take that text from the view (textfield or something) and return a result back to the view.
I want to use django only to give the script a webinterface. And it is only for me, maybe for a few people, not for a big audience. No deployment.
Edit: When I first thought the solution would be "Django", I asked for it explicitly. That was of course a mistake because of my ignorance of WSGI. Unfortunately nobody advised me of this mistake.