I do this for a living: design, prototype and take electronics to manufacture.
You need an electronics assembler / manufacturer. An example is http://www.asteelflash.com/ (no affiliation, but I've worked with them). Find a number of assemblers, bring them your design and ask them to quote for it. They will in turn ask you a number of questions, such as "How many?" and "Do you have funding for this?", before getting to technical questions related to testing and assembly. The smaller ones will let you have a little tour of the factory once they think you're a serious customer.
Asteelflash are probably suitable for the 250-10,000 unit range of production. There are smaller companies that will do smaller runs, usually a few guys in an industrial park in some corner of a city. You can have them hand-assemble for you, but the per-unit cost is quite high.
You need to work out a business plan as well, although that's beyond the scope of this site.