How to make a good impression on a Casting Director
I think this should be separated into two separate sections. How to make a good impression via email/letter and how to make a good impression in person.
When you are writing to a casting director remember to keep it relevant and to keep it brief, and if at all possible make it interesting. They are busy people and are contacted many times each day by actors. Put yourself in their position, if you had a lot to do on three separate projects you would only want to hear from people that had something relevant to say. General letters asking for non specific auditions are unwelcome, as are letters that just say hello I'm an actor. Avoid also anything that you might think is funny or cute such as adding presents or glitter or jokes. You're a professional.
On the other hand, if you have something relevent to tell them don't be afraid to get in touch. New showreel? Great, get in touch and send them a link, that is relevant and useful. They may not have time to watch it but it's a genuine reason to contact them. If you are in a production and want to make them aware of it then again, great, get in touch. It's their job to know who is out there and what they are doing and you just made it easier for them.
If you are writing asking to be considered for a job, you need to first make sure that your information is correct, i.e that they are actually casting the project, that you are available for all of the dates and that you really can believably play the character. If you apply for something you aren't really suitable for (we've all thought about it when times are quiet) you will annoy them and come across as naïve and unprofessional. Don't do it.
If you are sure you have all of the right information then keep the letter brief and to the point. Highlight any specific skills that would be relevant (combat skills for a Viking Warlord for example), include a C.V/headshot or a link to your Spotlight page and make sure you add a phone number. Then leave it alone. They will get in touch if they want to see you. Annoying follow up calls are not welcome.
If you are meeting a casting director in person, you can make a good impression by being on time, keeping calm and most of all, by being good. Do your homework on the script, make (interesting) choices about the character, be familiar enough with the text to be able to bring it off the page, and if they tell you to do or wear something specific, do it.
Staying calm can be tricky when you are new or haven't had many auditions for a while and really want the job. Just try to focus on and enjoy the work. Don't worry about trying to make them like you, try not to over evaluate what is happening in the room while you are in it, just talk person to person, be honest about your thoughts on the character/project and then do the audition as you have prepared it. Once it's done, make sure you have everything and leave, don't try and stay in the room any longer than they want you too, this screams trouble.
Try and have answers for frequent questions prepared and never be negative towards productions or colleagues you have worked with in the past. Show enthusiasm towards the project but make sure you're not just grinning and nodding like a loon the whole way through.
The main thing is though to have done your homework. If you are prepared, chances are you will be calmer and everything will fall into place. It's part of your job to be able to control your nerves, so work at it and turn them into positive energy instead.
Casting directors are just people, you can make a good impression on them by making their lives easier and being good at what you do.