What is the best way to start a personal statement?

A personal statement is meant to demonstrate your interest in your chosen degree subject and demonstrate how your skills are applicable to that subject, while also giving the university a small glimpse into who you are as a person. How you start a personal statement may depend on whether or not you are applying for a single/similar range of subjects, or if you are applying for several different subjects.
If you are applying for a single subject, one possible way to start is to tell them about the moment that first sparked your interest in that subject. It might not be more than a sentence or two, but it will be a good starting point to then show how that interest deepened to the point that you chose to do a degree in the subject. For example, you may have done a DNA profiling project at school and it made you realise some of the wider applications of genetics.
When applying for several different subjects, it may be more difficult to get started, but it is a good idea to find a common thread for all of the subjects. If they are more practically based, for example, you could start with how you like doing practical hands-on work, in the form of an example of something you did that involved manual labour.