Before you approach your dream actor:
Unless you're a household name, it's going to be challenging to convince a respectable actor that you can direct them in a feature film. So do something first - act in a short film, PA, take film/acting classes, write something wonderful, or make short films... create anything to show that you're serious.
Different ways to attach talent:
1) Direct connection - if you have a direct hookup to an actor of your choice, you can simply send off the great script you've put your heart and soul into, and hope they respond with enthusiasm! If they do, you can ask him/her to be verbally attached with no legal work at all (and before you have $). But you'll want a 'letter of intent' eventually, and that usually requires a legal attorney (even if it's just to write it up).
2) Letter of intent route - used to legally legitimise the actor's intent to be attached. This can be sent directly to the actor, or to the agent/agency, depending upon the actor's preference/situation. If you go the agency route, it will most likely cost money (i.e. casting director/producer(s) and/or legal attorney to help make deal with agent/agency - see 3).
3) Want verbally attached talent to be legally attached? Have casting director and/or legal attorney (route) communicate with the actor's agent, and work as a conduit between the actor and producer to make the deal.
And, remember - it doesn't matter if the actor is your friend or they are really, really interested... without a contractual agreement, nothing is concrete. Agents/agencies/managers can be great assets to the actor, but they are not looking out just for the actor - they want to make money, too. And no matter how nice they are, they do not work for You. :)
4) Already know the fab actor that's going to be in your film? - If you already have an established relationship with the actor that already wants to be in your film, they will most likely refer you to other actors/connections they have... other people they want to work with.
In my first short comedy, DropIt!, most of my ensemble cast was simply found from/through hiring a few solid actors. Thanks, Heath!
5) This is an extension of no. 4. - If you have an actor on board that has connections to a big agency, he/she may be willing/able to get you some (seasoned) names of possible leads who may be right for the part, and without you having to do no. 6 or 7.
6) If you have no connections, and a little money - You can ask your casting director and/or legal attorney to communicate with the agency in an attempt to reach out to the actor of your preferred choice... but if you don't have money to make an offer, you're probably wasting your time.
7) Have developmental funds to play with? - You can use some of this $ to hire an agency directly to aid you in attaching talent from their pool of resources. Realistically, it could cost your production thousands of dollars, and there's a possibility you may still walk away with no real results. But then again, if they do help you cast a recognizable face, I suppose it could be worth it...
8) Reach out approach - If you've been in this biz a while, chances are you know people who know people... there is no shame in asking friends with possible connections/fellow filmmakers if they have any actor recommendations. In most cases, they'll be happy to! I know I would jump at an opportunity to connect some of my very talented friends up with other promising projects. So, reach out, and don't be shy!
I urge you to not settle on talent no matter what. Have a standard, and don't compromise because of a bad day/mo./yr! IF you have good material, people will know it, and the talent will come.
Do yourself a favor, and don't stress or force this creative process. If anxiety's part of the equation, perhaps this is not the right person/deal/moment.
And as producer, Mynette Louie says, Don't Stop Believin'.
Happy Casting! Jentri