The simplest way would be to start from a new Visual Studio 2013 ASP.NET Web Application template. In the "New ASP.NET Project" dialog select "Web API" and then click "Change Authentication" button and select option "Individual user accounts" like the picture below:

This will create a project that uses the new ASP.NET membership "family member" ASP.NET Identity with a bearer token OAuth implementation.
What you need to look at are the following classes:
App_Start->Startup.Auth.cs
Token authentication is handled by OWIN middleware, here is the code that configures the pipeline. The most important is the call to UseOAuthBearerTokens which will enable 3 OWIN middleware components Authorization Server middleware, Application bearer token middleware, External bearer token middleware. You probably won't need the last one.
App_Start->IdentityConfig.cs
By default ASP.NET Identity is using Entity Framework as a storage provider (user, roles,claims persistance). If you will not use EF, you have to switch to another storage provider or implement it yourself with a couple of interfaces. Overview of Custom Storage Providers for ASP.NET Identity.
Providers->ApplicationOAuthProvider.cs
OWIN middleware will handle every request with the appropriate header. Here is the code that validates username and password provided in the HTTP header against a storage provider and returns the token which you will append to every subsequent HTTP request.
Authentication workflow
First you need to get the security token. This is the task of the OAuth authorization server. The token endpoint is configured to exist at http://yourSite/Token. To get the token you need to compose a special HTTP header (test it with Fiddler). The first 3 lines should go to the POST request header and the last one to request body.
Host: yoursite
Content-Type: application/json;charset=UTF-8
Content-Length: 51
grant_type=password&username=xxxxxx&password=xxxxxx
If the credentials are ok, you will receive the following response. Save the access_token value so that you will use it in step 2:
.expires=Tue, 17 Jun 2014 22:11:12 GMT
.issued=Tue, 03 Jun 2014 22:11:12 GMT
access_token=c-D34PHKFGaPthuF2sIwmeowXYAPFiSPsMH...
expires_in=1209599
token_type=bearer
userName=xxxxxxx
Compose a appropriate GET request to a secured resource with jQuery (use show response to see the whole response):
var getData = function(){
var url = "http://yoursite/api/protectedResource/";
$.ajax(url,{
type: "GET",
headers: "Authorization" : "Bearer " + accessToken
}).always(showResponse);
return false;
};
I hope this will get you started.