First thing I would do is download a copy of TestDriven.Net to use as a test runner. This will add a right-click menu that will let you run individual tests by right-clicking in the test method and selecting Run Test(s). This also works for all tests in a class (right-click in class, but outside a method), a namespace (right click on project or in namespace outside a class), or a entire solution (right-click on solution). It also adds the ability to run tests with coverage (built-in or nCover) or the debugger from the same right-click menu.
As far as setting up tests, generally I stick with the one test project per project and one test class per class under test. Sometimes I will create test classes for aspects that run across a lot of classes, but not usually. The typical way I create them is to first create the skeleton of the class -- no properties, no constructor, but with the first method that I want to test. This method simply throws an NotImplementedException.
Once the class skeleton is created, I use the right-click Create Unit Tests in the method under test. This brins up a dialog that lets you create a new test project or select an existing one. I create, and name appropriately, a new test project and have the wizard create the classes. Once this is done you may want to also create the private accessor functions for the class in the test project as well. Sometimes these need to be updated (recreated) if your class changes substantially.
Now you have a test project and your first test. Start by modifying the test to define a desired behavior of the method. Write enough code to (just barely) pass the test. continue on with writing tests/writing codes, specifying more behavior for the method until all of the behavior for the method is defined. Then move onto the next method or class as appropriate until you have enough code to complete the feature that you are working on.
You can add more and different types of tests as required. You can also set up your source code control to require that some or all tests pass before check in.