I am going to assume that by questionaire you mean survey (i.e. one that pops up or that you send out by email).
In terms of getting people to respond to such a questionaire the key thing is to keep it short and allow them the opportunity to end it and any point i.e. without quitting and losing all the data!
In all the questions try and do the work for them - so they can respond with a minimal number of clicks.
Generally surveys start by finding out a bit about who the user is e.g. How long they have had a smart phone, do they rate themselves as technical, male/female, if you go for age do it in buckets so that people don't have to identify their exact age. But again limit it to just what will be useful to you.
For the questions themselves you should generally ask closed questions e.g. where they can select one from three answers or use a rating scale (with a slider or radio buttons).
So to rephrase some of Jimmy's questions:
How true are these statements:
- "I always knew where to click"
- "I know where to
- "This product felt trustworthy"
- "This product is attractive"
- "I felt lost"
There are lots more examples of question type here.
You can probably get away with one or two open questions. Although you could provide an add comment button next to each statement ... in case they felt they wanted to add an explanation.
To get an initial set of questions to ask I would brainstorm with my colleagues to find issues that will affect design decisions. Identify some questions. Then walk through your best guess at the answers ... would that information be useful to you? What would you do with it? What if the answer was the opposite. What would you do then?
The only way to test out your questionnaire is to pilot it with a few users (could be anyone someone in your office, friends...). This is the best way to fine tune what needs to be asked.
The queen of forms and questionaires has to be Caroline Jarrett - here is a great slideshow she did on designing surveys in 2011 and this one in 2012 (read both they are different).
Here is a podcast on surveys from April 2012.
Designing an effective questionaire is also about asking them in the write way and well designed. Caroline's book forms that work has to be the key reference here too.
Dave Travis has also put together some good advice:web survey design step by step; 20 tips for web survey design.
I also like funnel and Fast Company's take on it.
For instance the picture below demonstrates lots of best practice for mobile. I love how the question is the focus and is very large (no fiddling around to press tiny buttons). I think the use of a slider control with a big button is great (notice how minimal they have been with the data ink on the scale). I assume they swipe to move on. Notice how the user can submit at any point. I would probably have added a number of steps e.g. 1 of 5. to encourage them to get to the end. Otherwise perfect.