Is there anything I could write for "experience" on a job application, if it is my first job?

Mention them and smarten the job description up a bit.

Any clubs that you were on in school. Any involvement in students union, or a paper route.

Skip the title, “experience” and write in relevant “skills”

Taking care of home and family involves a number of skills. Have you done any volunteer work? An employer can appreciate seeing an applicant who knows they can apply practical life skills to their job. If you have five kids, and your home runs smoothly, say so, then point out that this speaks to your organizational skills, delegation of tasks, supervisory skills. Are you the bill payer, do you file your own taxes?
Your day to day life is experience, but most people don’t think to mention that.

I agree with @Jonesn4burgers. Also list your interests and hobbies and what you’ve done to further them. If you’re a reader, for example, list a few books that have impressed you. Or if you’re an athlete, talk about any events you’ve competed in or won. Or if collect coins or stamps or play a musical instrument, talk about that. In fact, talk in your resume about anything that will give the interviewer an idea of who you and what your value might be to the company. A side benefit of adding this kind of information is that it gives you a chance to showcase your writing and communication skills… skills which are important to a company in any job you seek.

This question indicates that you are about to turn 16. What did you end up doing last summer? No one expects you to have had any job experience. The above advice, particularly that from @Pachy, about skills is good.

Tell your prospective employer that you are responsible, hard-working, energetic, a quick learner and pleasant to have around.

Be honest and simply say new to the work force and eager to learn new skills. Also list any skills you may have mastered and hobbies you love and why you want to work at the company you are applying to and how they would benefit from you working there. Then express your visions for your future and why and how this job will help you achieve your vision. Good luck!

If you have no prior work experience just be honest and tell them that. Interests, skills and hobbies that might be relevant to the application would be good or just anything in general you’re good at. Tell them you’re willing to learn and work hard. And that you’re willing to work any time they need you to. That should impress them.