Don't shoot handheld and don't use a phone.
Baring that, use stabilization such as a steadicam or steadicam jr (if using a tripod really isn't an option), use lots of well controlled lighting (phone cameras suck at low light) and plan your shots out very carefully. Use external audio recording rather than the phone's built in mic and do a lot of grading of the color in post. By the time all is said and done, getting a better camera is likely a cheaper option for the most bang for your buck, though any camera would benefit from the other mentioned options.
It is exceptionally hard to get a professional quality result out of using a phone camera. There is a very valid reason that most decent video camera costs more than your average smartphone, and the camera in a smart phone is a very small portion of the actual cost of the phone.
There have been projects where smartphones were used to produce professional results, but these have more been marketing gimmicks done by experienced professionals and it made their lives more challenging rather than easier. Trying to get similar results without a lot of experience is going to be quite challenging.