For testing we now create a testing module using TestBed. We can use the TestBed#configureTestingModule and pass a metadata object to it the same way we would pass to @NgModule

beforeEach(() => {
  TestBed.configureTestingModule({
    imports: [ /* modules to import */ ],
    providers: [ /* add providers */ ],
    declarations: [ /* components, directives, and pipes */ ]
  });
});

For routing, instead of using the normal RouterModule, we would instead use RouterTestingModule. This sets up the Router and Location, so you don't need to yourself. You can also pass routes to it, by calling RouterTestingModule.withRoutes(Routes)

TestBed.configureTestingModule({
  imports: [
    RouterTestingModule.withRoutes([
      { path: 'home', component: DummyComponent }
    ])
  ]
})

To get the Location and Router in the test, the same thing works, as in your example.

let router, location;

beforeEach(() => {
  TestBed...
});

beforeEach(inject([Router, Location], (_router: Router, _location: Location) => {
  router = _router;
  location = _location;
}));

You could also inject into each test as necessary

it('should go home',
    async(inject([Router, Location], (router: Router, location: Location) => {
})));

The async above is used like done except we don't need to explicitly call done. Angular will actually do that for us after all asynchronous tasks are complete.

Another way to get the providers is from the test bed.

let location, router;

beforeEach(() => {
  TestBed.configureTestingModule({
    imports: [RouterTestingModule.withRoutes([
      { path: 'home', component: DummyComponent }
    ])],
  });
  let injector = getTestBed();
  location = injector.get(Location);
  router = injector.get(Router);
});

Here's a complete test, refactoring your example

import { Component } from '@angular/core';
import { Location } from '@angular/common';
import { Router } from '@angular/router';
import { RouterTestingModule } from '@angular/router/testing';
import { fakeAsync, async, inject, TestBed, getTestBed } from '@angular/core/testing';
import { By } from '@angular/platform-browser';

@Component({
  template: `
    <router-outlet></router-outlet>
  `
})
class RoutingComponent { }

@Component({
  template: ''
})
class DummyComponent { }

describe('component: RoutingComponent', () => {
  let location, router;

  beforeEach(() => {
    TestBed.configureTestingModule({
      imports: [RouterTestingModule.withRoutes([
        { path: 'home', component: DummyComponent }
      ])],
      declarations: [RoutingComponent, DummyComponent]
    });
  });

  beforeEach(inject([Router, Location], (_router: Router, _location: Location) => {
    location = _location;
    router = _router;
  }));

  it('should go home', async(() => {
    let fixture = TestBed.createComponent(RoutingComponent);
    fixture.detectChanges();
    router.navigate(['/home']).then(() => {
      expect(location.path()).toBe('/home');
      console.log('after expect');
    });
  }));
});

UPDATE

Also, if you want to simply mock the router, which actually might be the better way to go in a unit test, you could simply do

let routerStub;

beforeEach(() => {
  routerStub = {
    navigate: jasmine.createSpy('navigate'),
  };
  TestBed.configureTestingModule({
    providers: [ { provide: Router, useValue: routerStub } ],
  });
});

And in your tests, all you want to do is test that the stub is called with the correct argument, when the component interacts with it

expect(routerStub.navigate).toHaveBeenCalledWith(['/route']);

Unless you actually want to test some routing, this is probably the preferred way to go. No need to set up any routing. In a unit test, if you are using real routing, you're involving unnecessary side effects that could affect what you are really trying to test, which is just the behavior of the component. And the behavior of the component is to simply call the navigate method. It doesn't need to test that the router works. Angular already guarantees that.