If you are looking to venture in to a new career you may need to gain some experience in the field first. Many employers look for someone with the relevant qualifications but if will often favour a candidate if they have experience in the same or similar job role as what is being advertised.
For some people, leaving an employed job to take up voluntary work to gain experience is simply not an option but you could always look in to doing work at weekends or in the evening. Other people chose to dropdown to part time hours in their existing role to allow them the time to train for a new career.
If you have found a job that you believe you are highly qualified for but lack the experience, why not call up the employer and ask to come in for a chat. You may have to take a slight drop in salary until they are satisfied that you can do the job, but it is often a quicker way in to the role that you have wanted.