ASP.NET Web API REST Querystring - How does a client know available parameters and options?

You have some options to do this, let's try to help:

1) Configure a generic route to asp.net web api knows how to solve another action's name different from Get to a get method, on the App_Start\WebConfigApi.cs class, try to add this:

config.Routes.MapHttpRoute("DefaultApiWithActionAndId",
            "api/{controller}/{action}/{id}",
            new { id = RouteParameter.Optional });

Using it, you can have diferent methods on the api controller:

// request: get
// url: api/Students/GetStudents
public HttpResponseMessage GetStudents() 
{
   return Request.CreateResponse(...);
}

// request: get    
// url: api/Students/GetStudentsWithJobOffer
public HttpResponseMessage GetStudentsWithJobOffer() 
{
   return Request.CreateResponse(...);
}

// request: get    
// url: api/Students/GetStudentsAcceptedJob
public HttpResponseMessage GetStudentsAcceptedJob() 
{
   return Request.CreateResponse(...);
}

2) Use a simple parameter on the Get method:

// request: get
// url: api/Students?jobOfferStatus=1       
public HttpResponseMessage GetStudents(int jobOfferStatus) 
{
    // use jobOfferStatus parameter to fill some list
   return Request.CreateResponse(...);
}

3) Use a simple method with a parameter named id, to get a default friendly url by asp.net mvc web api.

// request: get
// url: api/Students/1      
public HttpResponseMessage GetStudents(int id) 
{
    // use the id parameter to fill some list
   return Request.CreateResponse(...);
}