How to become a professional actor
First of all you should try to get some acting training. Either a BA in Acting or Diploma in Acting, or a postgraduate course if you have already completed a related degree. Look up the NCDT website for accredited courses. You will have to audition for a place, and the preparation can be quite intensive. This will give you some professional standing, you can become a student member of Equity and spotlight, and quite often you will be introduced to agents, casting directs and directors whilst on the course.
A professional actor needs to be on Spotlight as this is where most of the main casting for TV, Film, Commercial and Theatre takes place. To be on it you either need professional credits or professional training. A good way to gain professional credits if you are not lucky enough to get a good agent straight away is to join up with Casting Call Pro, Cast Web or CastNet and apply for jobs on there using your drama school credits at first before you have built up professional ones.
Some people start out through being a child actor, as there are more likely to be open auditions for that age group. But even in this instance it is a good idea to undertake some form of training at The Actors' Centre to help with specific skills to for a longevity of career.
If you can't afford to go to drama school full time, there are lots of evening classes and summer schools at drama schools which may then help you to get your first short film or fringe theatre role which you can build on with experience. One you have your first few roles then you will be considered for many more. Training, even if brief, is the key, however. Good luck!