I think it is expected that most PhD students do not have prior experience apart from their PhD. Many PhD graduates were in your shoes and got Postdoc positions. A career advisor advised me to start my CV with most important details rather than my post code, etc. You may start with your publication list, then education, then awards (PhD scholarship). Nevertheless there is usually career counselling service at the university. Use it and you will get useful tips for filling CV and cover letter. All the best.