What is the best way to outsource development of a ...

I would reccomend Elance.com, ODesk.com or rentacode.com

there are many companies all around important to c if they have a designer and developers (both capabilities) just contact their previus customers to get testimonials

A lot depends on what you want. If you are a large corporation or a small business. It also depends on what part of the website you want to outsource ... the design, the code, the database, the whole bag of wax? If you are a midsize company and would like for the whole thing to be done check the local web design companies. A lot also depends on how much money you have for this project. First, make sure you know what you want. Then take a look at your budget. Then check on your in house expertise. Then start casting around to local web designers. Make sure you get recommendations and check them out.

You could go with something like

type your requirements into google, i.e. web design or graphic design click onto the top 20 and review their online portfolio, if you have specific requirements make sure that they are met and then arrange to meet a few of the companies, see whether they can create what you want, timescales, costs, changes and support they offer.