Create the solution

Create a new solution following File -> New -> Project -> Web, then choose ASP.NET Web Application. Name it with Demo. Then in the upcoming dialogue box, choose Empty and check Web API, click OK.

Install NuGet packages

Run the following command in the Package Manager Console.
PM> Install-Package Microsoft.AspNet.OData

Add Models

In this getting-started example, we just add two model class Person.cs and Trip.cs under folder ModelsPerson can navigate to Trips.
using System;
using System.ComponentModel.DataAnnotations;
namespace Demo.Models
{
    public class Person
    {
        [Key]
        public String ID { get; set; }
        [Required]
        public String Name { get; set; }
        public String Description { get; set; }
        public List<Trip> Trips { get; set; }
    }
}
using System;
using System.Collections.Generic;
using System.ComponentModel.DataAnnotations;
namespace Demo.Models
{
    public class Trip
    {
        [Key]
        public String ID { get; set; }
        [Required]
        public String Name { get; set; }
    }
}
The attributes [Key] and [Required] are all from System.ComponentModel.DataAnnotations meaning the property is key and required seperately.

In-Memory data source

This tutorial uses in-memory data source, which is more flexible. Below are only one way to implement, you can definitely have your only way.
Add a folder DataSource and add a class file DemoDataSources.cs with the code below.
using Demo.Models;
using System.Collections.Generic;
namespace Demo.DataSource
{
    public class DemoDataSources
    {
        private static DemoDataSources instance = null;
        public static DemoDataSources Instance
        {
            get
            {
                if (instance == null)
                {
                    instance = new DemoDataSources();
                }
                return instance;
            }
        }
        public List<Person> People { get; set; }
        public List<Trip> Trips { get; set; }
        private DemoDataSources()
        {
            this.Reset();
            this.Initialize();
        }
        public void Reset()
        {
            this.People = new List<Person>();
            this.Trips = new List<Trip>();
        }
        public void Initialize()
        {
            this.Trips.AddRange(new List<Trip>()
            {
                new Trip()
                {
                    ID = "0",
                    Name = "Trip 0"
                },
                new Trip()
                {
                    ID = "1",
                    Name = "Trip 1"
                },
                new Trip()
                {
                    ID = "2",
                    Name = "Trip 2"
                },
                new Trip()
                {
                    ID = "3",
                    Name = "Trip 3"
                }
            });
            this.People.AddRange(new List<Person>
            {
                new Person()
                {
                    ID = "001",
                    Name = "Angel",
                    Trips = new List<Trip>{Trips[0], Trips[1]}
                },
                new Person()
                {
                    ID = "002",
                    Name = "Clyde",
                    Description = "Contrary to popular belief, Lorem Ipsum is not simply random text.",
                    Trips = new List<Trip>{Trips[2], Trips[3]}
                },
                new Person()
                {
                    ID = "003",
                    Name = "Elaine",
                    Description = "It has roots in a piece of classical Latin literature from 45 BC, making Lorems over 2000 years old."
                }
            });
        }
    }
}

Add Controllers

Since there are two entity set, we will add two controller class under the folder Controllers
First is controller for People
using Demo.DataSource;
using System.Linq;
using System.Web.Http;
using System.Web.OData;
namespace Demo.Controllers
{
    [EnableQuery]
    public class PeopleController : ODataController
    {
        public IHttpActionResult Get()
        {
            return Ok(DemoDataSources.Instance.People.AsQueryable());
        }
    }
}
Then is the controller for Trips
using Demo.DataSource;
using System.Linq;
using System.Web.Http;
using System.Web.OData;
namespace Demo.Controllers
{
    [EnableQuery]
    public class TripsController : ODataController
    {
        public IHttpActionResult Get()
        {
            return Ok(DemoDataSources.Instance.Trips.AsQueryable());
        }
    }
}
In this very simple implementation, only simple Get with query options are allowed. If you want to enable more capabilities in your controller, the code is quite similar with what's done with EF as data source. Please refer to ASP.NET Web API OData V4 Samples and Create an OData v4 Endpoint Using ASP.NET Web API 2.2.

Configure the Endpoint

The last step is to modify the WebApiConfig.cs file under App_Start.
using Demo.Models;
using Microsoft.OData.Edm;
using System.Web.Http;
using System.Web.OData.Batch;
using System.Web.OData.Builder;
using System.Web.OData.Extensions;
namespace Demo
{
    public static class WebApiConfig
    {
        public static void Register(HttpConfiguration config)
        {
            config.MapODataServiceRoute("odata", null, GetEdmModel(), new DefaultODataBatchHandler(GlobalConfiguration.DefaultServer));
            config.EnsureInitialized();
        }
        private static IEdmModel GetEdmModel()
        {
            ODataConventionModelBuilder builder = new ODataConventionModelBuilder();
            builder.Namespace = "Demos";
            builder.ContainerName = "DefaultContainer";
            builder.EntitySet<Person>("People");
            builder.EntitySet<Trip>("Trips");
            var edmModel = builder.GetEdmModel();
            return edmModel;
        }
    }
}

Try with it

It's done to create a very basic OData endpoint with in-memory data source using Web API OData. You can try it out now! All samples below are all GET method.
Service document
http://localhost:[portNumber]/
Service metadata
http://localhost:[portNumber]/$metadata
Get People
http://localhost:[portNumber]/People
Queries
http://localhost:[portNumber]/People?$filter=contains(Description,'Lorem')
http://localhost:[portNumber]/People?$select=Name
http://localhost:[portNumber]/People?$expand=Trips