You have to initialize the form instance with values from the request:
from flask import request
@app.route('/contact', methods=['GET','POST'])
def contact():
form = ContactForm(request.form)
if request.method == "POST" and form.validate():
# do something with form
# and probably return a redirect
return render_template("contact.html", form=form)
Here's a better tutorial than the one you link in your question: http://flask.pocoo.org/docs/patterns/wtforms/.
Have a look at the template rendering code in the tutorial, make sure you render the form field errors. If the form is posted but does not validate the code will fall through to render_template
with the form instance containing field validation errors (again, see the tutorial and WTForms documentation for details).