The restaurant owner who hired me asked me to call back every week. After five weeks of calling, I finally landed my first part-time job. I worked around 30-35 hours a week and eventually got promoted to a cook. I stayed there for three years, which allowed me to save money for my first car and learn valuable life lessons.
I would definitely suggest checking out your local labor laws in the state that you live in. If you don't know of anyone that's hiring 14 year olds, there's a good chance there's labor laws prohibiting 14 year olds from working. However, if you check and see that there are no laws prohibiting that, I would suggest calling to some places to see if they hire 14 year olds. I know where I live there is a local grocery chain that hires that age, as well as a coffee chain that hires as well.
There are other ways of making money at this age that doesn't require an actual job though. Helping neighbors with tasks like lawn mowing, planting flowers, car washes, etc. The older generations appreciate young kids that are willing to put in some elbow grease to earn extra cash.
I hope this helps!