If you are interested in a career in patent law (a decision not to be taken lightly), then the effort you put into preparing your applications and for subsequent interviews is vital. Having finally found myself a training position with a firm of patent agents, I'll try to share with you what worked for me.
Initially I gathered as much information as I could on the profession and found that an excellent starting point was the Inside Careers  guide to Chartered Patent Attorneys. This publication offers a comprehensive guide to the profession and includes sections on training and development, career paths, and autobiographical descriptions from patent agents at various stages in their career. I also found information at my university careers library and made contact with a local patent attorney through a careers talk organised by my department.
It helps to make full use of the opportunity to talk to people in the profession, particularly those in training. University careers services often have talks by patent agents and these offer a valuable insight into the job. I was able to arrange a meeting with a second patent agent I heard give a careers talk. With him I went over specific questions in more detail and discussed applications. I also attended an open day run by patent firm Mewburn Ellis . Details are available on their application forms and they usually hold these each autumn, in Bristol, London, and Manchester. This involved a number of sessions ranging from the basics of intellectual property to actually preparing short descriptions of various objects such as a light bulb, in 'patent terminology'. There was also plenty of opportunity to talk to various staff and ask questions.
Arranging some work experience may prove harder as patent agents are very busy people! But it's well worth doing, so make the most of the contacts you have made in the profession. I was able to arrange a day's work shadowing through a patent agent I met whilst participating in the Biotechnology Young Entrepreneurs Scheme . This competition involved working as a team of young scientists to form a virtual biotech company and gave me the experience of investigating how to best protect the product our company was offering. I was also very lucky to arrange a week's work experience at a firm in London where I was given patent applications to review and infringement cases to look over. This was invaluable experience and certainly prepared me for interviews!
Having done my research, it was time to apply. The first decision I made was to apply to patent firms, i.e. private practise, rather than an 'in house' department at a pharmaceutical company. It's generally acknowledged that you get a broader training in private practise than in industry because of the wide range of matter you deal with in a firm, and this is necessary to pass the qualifying exams.
In both my covering letter and CV I stressed a wide scientific background and also detailed my foreign language skills. Basic knowledge of languages such as French, German, and even Japanese are important, although you don't need to be fluent. Ensure your applications are to firms which practise in your discipline, in my case biotech, otherwise you will receive a straight rejection. A tip given to me by a trainee patent agent is to include a piece of written work, such as a short description of a kitchen implement (mine was about 100 words), with your application. Some firms may require this, but it will emphasise your interest to other firms. I read a number of patents before preparing this, which I found by using an intellectual property site  on the Internet. In addition, most large cities have a technical library where patents are available.
Despite having talked to many trainee patent agents, no one could advise me on a 'good time of year' to apply. In the end, influenced by when I would be finishing my Ph.D., I sent my first batch of applications off in early autumn. I continually monitored the Web sites of various firms and the Inside Careers Web pages on key recruiters, checking for any adverts or application deadlines, and I would start doing this at least a year before you want to start your job. I also checked New Scientist and Internet job sites for adverts. I bought a copy of the UK Directory of Patent agents published by the Chartered Institute of Patent Agents  and this enabled me to target my applications to specific firms and regions of the country. If you don't know who to address your covering letter to, call up the firm or company and ask. The majority of patent firms are based in London, but there are provincial firms, so if you want to work in a particular area then target these firms first.
I sent my applications off in stages, initially targeting firms in the north of England. Some trainee patent agents I spoke to sent off in excess of 80 applications and this appears to be normal! Most firms will reply, usually to let you know they have filled their training places and these come within a few days of applying! Slower replies can be more promising and will hopefully result in an interview.
So finally I had my first interview. My advice is to be prepared for almost anything! I was asked to talk about projects I'd completed as an undergraduate, which stretched my memory! You also need to be able to explain your current research in simple terms, e.g., to the person sitting next to you on the bus. I was asked this at every interview. For general preparation I made sure I was aware of the different types of intellectual property besides patents and read up on various topical issues such as gene patenting. Basically, the more you know about the profession the better. It is important to be aware of how long it takes to train and that the exams are very difficult! Most interviews will last an hour, although one of mine lasted for nearly three! Besides the usual questions of 'why do you want to be a patent agent?' I was generally asked about my academic work and why I was suitable for the job. In addition, I was often asked to explain various techniques and even mechanical objects in simplified terms, so that someone with no prior knowledge would understand. As with all interviews, make sure you have some good questions to ask at the end.
It took me a few attempts before I was successful in securing a second interview. Luckily that went well and I was offered the job. Given the competition for patent traineeships, it was not a difficult decision to accept it!