How to get un-solicited scripts seen by producers
An un-solicited script is a very difficult thing to promote, but it is not impossible!
The best way forward is to attend as many writing workshops, networking events, film festivals, etc as possible, do not be afraid to approach people, but also be aware that they may be busy and you may be viewed as a nuisance, if you get the slightest hint your presence is surplus to requirements, move on...you wont endear yourself to anyone by outstaying your welcome.
When attending events, don't start with the 'I have a script' line...its something they have heard a million times before. Learn something about them if you are approaching informally before discussing your project, then you can try and speak about your ideas. If you are approaching someone officially, then practice your pitch, and make sure you have a catchy opening few lines...if you don't have their attention in the first 10 seconds...you've lost!
If you have friends who also have friends who know people, then don't be afraid to network through friends, but also do not forget these friends if things go really well...always show gratitude to those who put you where you are.
There are some agents who will accept unsolicited material, but do your research carefully first, find out who accepts the work, WHEN the work is accepted (many agencies only accept this kind of work during certain times of the year), and ensure that what you send is fully compliant with their requirements. You may have a lot of hoops to jump through, but if you feel your work is worth it, then you wont mind.
One final piece of advice which can easily be overlooked...BEFORE you show your script to ANYONE...get it COPYRIGHTED! Do not send it registered post to yourself, if anything goes to court, a half decent solicitor can pull your claim to pieces! Copyright it with a professional solicitor...preferably one who specializes in this kind of thing.
Good luck, and no matter what...don't give up! Have faith in yourself and faith in your work, if you truly believe in it, then it will be easier to convince others its worth believing in.