How to find a reputable agent
Finding a reputable agent is difficult. Most actors I meet often say how they rarely get work from their agent, but occasionally I meet actors who get a lot of good work from their agent. The key to getting a reputable agent is based on sound research and demonstrating your skills. Some agents only specialise in certain areas (e.g. musical theatre), which might not be clear at first and might not be your line of work.
Firstly, identify the type of work you want to do i.e. musical theatre, TV, presenting, touring, corporate, film etc. The more you can do, the better. Identify what skills you have e.g. combat fighting, horse riding, working at heights, musical instruments (again, the more skills you have, the better). And identify your criteria for an agent i.e. do you want regular work or work at certain times of the year etc.
Conduct research, actively speak to other actors you have worked with or are currently working with and go to networking events like Perform 2013 etc. By speaking to other actors, you'll gain an understanding of which agencies meets your criteria i.e. gets you regular work, pays on time, has lots of contacts etc. Make a list of agencies and which ones tick your boxes.
Another research tool for identifying reputable agents is by looking at their websites and checking the profiles of their actors. For example, if they have a small selection of known and successful actors, then they are generally a good agent to go for. If they have hundreds of actors that aren't listed on IMDB, Spotlight or CCP, then this may be a less desirable agent. Also check the quality of the website in terms of layout and navigation and date last updated - this also provides a hint at their level of professionalism.
Once you have identified a number of reputable agencies, you have two options, 1). Write to them asking for representation or 2). Invite them to a play you are in and ask for reputation. The best method is to get into a play and then invite them along. Try and getting into a play that has a high profile, is close to their offices (i.e. central London) and a play with a number of performance dates to give them optional dates for attending. In either case, applications by post is much better than email as emails can be mislaid or easily deleted, but check the agency's website as this sometimes advises of application requirements or whether their books are open.
When writing to the agent by post or email, send your CV, and at least one 10x8 good quality headshot (usually one full body shot and one headshot) with your contact details printed on the back (this means if they loose your cover letter and contacts, they would have your contacts easily referenced on the back of the headshot). Provide a cover letter or cover email that explains why you want to be represented by them. Do a bit of research and determine what they are looking for and include this in your cover letter. Explain your skills and your successes in your acting career. Be careful not to make the cover letter or cover email too long, keep it short and punchy. Try to avoid asking agents to send headshots back as this will only annoy them. Finally, only write to the agency once, don't keep calling or writing letters as this will also annoy them. If you are doing a play and you have sent your CV, headshot and cover letter, you can always send a reminder closer to the performance date.