In the UK there are a lot of good programmes for engaging the public with mathematics, some of which have been touched on in other answers. Here is a list of the ones I think have worked the best or been most innovative:
1) Royal Institution Masterclasses: a UK-wide series of masterclasses aimed at age 13 school pupils. Classes are on Saturday mornings for between 5 and 10 weeks. Each class has a different presenter and each class lasts for 2.5 hours with time for lectures, exercises and refreshments. I've been involved in giving the Edinburgh and Glasgow masterclasses and they are a lot of fun for all involved. The kids really appreciate getting to see some maths that they'd never encounter through school, and especially enjoy seeing the diversity and usefulness of the subject. (In addition, a set of masterclasses gets broadcast on the BBC every Christmas!)
2) FunMaths Roadshow: a collection of 350 maths activities, each suitable for a particular age group between 5 and 20. The resources are cheap and easy to make, as well as being easy to transport, so that they can be taken all around the local area and used with different groups of people.
3) Maths busking: a new phenomenon which has been surprisingly successful! 'Buskers' go out onto the streets and perform games and tricks which appear to be magic but which can be explained by mathematics. It's a great way to engage with people who would otherwise never attend a maths lecture or think of going to a science museum.
4) Mathematical walking tours: do a tour that opens people's eyes to the mathematics around your city. This can be historical curiosities, geometrical constructions in the architecture or optimization in the town planning. Such tours are currently being designed for Oxford and London, or get examples from Manhattan or this maths tourism blog.
Whatever you decide to do, just go ahead and do it with plenty of enthusiasm! Good luck!
