Once you have followed the Route path and have reached the end point, or the start point if the Route is a loop, you will earn the Route Badge in Pokémon GO

A Route is a pre-defined path that you can follow while exploring. These paths may be made by Niantic, official partners or other Trainers, like you!

As you follow a Route, you may discover Pokémon and Items, and completing Routes will grant you rewards. Completing a Route will earn you the badge associated with that Route, featuring a custom photo from the start or end point.

You can see a list of nearby Routes by tapping on the Binoculars menu and tapping on the Route tab. This will show you nearby locations that serve as Route start points. Tap the See Nearby Routes to expand the map and see a list of available Routes.

As you are browsing the Routes list, you can tap on the flag button in the bottom right corner to sort the list by other options. By default, the list will show Routes that are nearest to you.

Tap on a Route to preview it and review the details. You will be able to see how many other Trainers have followed that Route, how many times you have followed the Route, the distance and the approximate amount of time it might take to complete the Route.

Scroll down this page to see Trainer-provided details, including a description of the Route, any Route Tags that have been added to the Route, elevation changes and the original Route creator.

To return to the list of Routes, tap the exit button in the top left corner.

Once you have found a Route and you are ready to begin, tap the Follow button. Note that the Route will not begin until you have moved close enough to the Route start point. A message will appear on the Map View if you are too far away.

The Route start point will feature a blue flag above the Poké Stop on the Map View. The Route will start automatically once you are close enough to the start point. Note that if you are already close enough to the start point, the Route will begin right away.

Follow the path marked on the Map View to follow the Route. While you are following the Route, the path will change color to show your progress towards completing the Route. Some Routes are able to be followed one-way only, while others can be followed in reverse or are a loop. These options are determined by the Route creator during the creation process. Tap the Route icon above the Binoculars menu at any time to see your active Route’s details.

Pause the Route at any time by tapping the Pause Route button on this page. If you pause a Route, you will need to return to your paused location and tap this button again to resume the Route.

To quit the Route, you can scroll to the bottom of the Route details screen and tap the Quit Route button. You will exit the Route once you tap Quit Route again on the confirmation screen.

Once you have followed the Route path and have reached the end point, or the start point if the Route is a loop, you will earn the Route Badge! Similar to a Gym Badge, each Route has its own individual Badge that features an image from the start or end point. Complete the same Route multiple times to level up your Route Badge. You can see all of your Route Badges on your Trainer Profile under the Routes section.

After you have reached the end point, you will see a confirmation that you have completed the Route and details of any item rewards you have received for completing the Routes. The Route title, badge and rewards will be recorded in your Journal.

The last step in completing the Route is to give the Route a star rating. Your rating will be used to assess the quality of the Route, but will not be shared publicly. If you have previously given that specific Route a rating, you will not see this screen.

Note that it’s possible to reach the end point of the Route but not complete the Route. This may occur if you didn’t follow the exact path set by the creator. To complete the Route in this case, resume the Route and continue to follow until you have traveled the full Route distance.

If you find a Route that is in violation of the Niantic Terms of Service or Player Guidelines, you can submit a report to the Niantic team directly from within Pokémon GO.

From the Route details screen, scroll to the bottom and tap on Report Route. You will be asked a series of questions to gather sufficient information to perform an investigation into the Route. Once you have submitted your Report, note that you may not hear back from Niantic regarding the status of your Report or any action that is taken in response.

You can also report a Route from the rating screen by giving a Route a 1-star rating and tapping the Report Route button.

Source: Official Pokémon GO support page