I don't think there are any absolute hard and fast rules, but a few pointers:
1. Before you even consider writing to the agent, do your research properly. As well as finding out whether or not the agent is bona fide (try and track down their website, ring them to enquire directly, check their status using the CCP tools, try and mail actors already represented by the agent to ask how they find the agency etc. etc.), you should be paying attention to whether or not their books are open, and what sorts of clients they already represent, as well as what sort of work they appear to specialise in. An agent whose books are open is more receptive to applications (because they are actively looking to take on new faces) then one whose books are said to be closed (in truth, no agency ever wholly closes the books, but those with closed books will not be looking to take people on the basis of unsolicited applications, at least - they might consider taking you on if they were to see you in something and like the performance). An agent who already has someone on the books who looks like you and performs the sort of parts you would perform is unlikely to take you on because they will consider a clash inevitable, and will feel this undermines their relationship with their current client; an agent who doesn't possess someone of your 'type' will often be more receptive because they want a wide range of casting choices available to cover every eventuality. It is also fairly obvious that if you are, say, a Musical Theatre specialist, and you apply to an agency who specialise in feature film work, it is less likely that you are going to be seen to have anything to offer them, whereas a specialist MT agent may highly rate your skills etc. So, choose who you write to intelligently.
2. Keep any cover letters brief, and to the point. There needs to be enough contained for you to make some kind of impression as a personality, but no-one has time to read five page introductions.
3. Things to emphasise may include: any hints at to what you think your casting type may be, the sort of roles you have played or see yourself playing, any training or experience you have if you have not yet really embarked on a career, and maybe even something interesting about you as a person etc . Just enough to whet their interest, because most of these details should be contained in the CV and headshot, but giving pointers to the agent and showing you have an idea of what you may offer is often a good move, because it allows the agent to recognise that you are thinking, as they are, of how you might be best be used as a saleable commodity/personality.
4. If you have never had an agent before, there is no shame in stating that you are looking for representation for the first time, and this is what you believe you have to offer. Agents will see you as good potential new talent.
5. Agents do like to see you working - therefore, it is always best if you can to couple a letter with an offer of something in which the agent can see you - generally, an invite to a show, but if you have any footage from screen material or a website or any thing relevant streamed online or good past reviews etc. then mention this, because it is something that the agent can then view at their own discretion. Very often, they *won't* take up the offer to e.g. attend a show, because they are busy people and coming to see you directly is an expenditure of effort and energy which may not pay off for them or which they feel is slightly unnecessary (sometimes they may surprise you!), but by showing you are working, you automatically rise higher in their estimation as an actor who can find employment. The sort of actor who tends to need an agent in order to *get them work* (i.e. who cannot find any work on their own, and so must rely on an agent to find it for them) is not of much interest to the agent, so always give agents examples of work if you can. This is not quite the same thing as saying that most jobbing actors get their best paying work through their agents, and tend to only find more minor jobs for themselves (unless their contacts are fantastic, personally) - that is pretty much a given, and many agents, once they take a client on, are more reluctant for them to do low paid work that may get in the way of the higher paying opportunities they are putting forward the actor's way. Some actors will say that once you have an agent, it is in your best interests to cut down on the low paying work. But until you have one, being seen to work (in whatever capacity) is preferable.
