So it appears that after you set up a buddy, there will be some new screens inside your trainer profile. To assign a buddy: click on your trainers avatar, then the menu at the bottom right, choose “Buddy”, pick a buddy from your list of Pokemon.
To check buddy progress: click on your trainers avatar, then the menu at the bottom right, choose “Buddy”. Now you will see the buddy progress towards earning extra candy. Here you see I would have to walk 3km for 1 candy. That’s a lot of hard earned candy!
From what I can tell from some quick research is that the distance necessary to get a certain candy is tied to the rarity of the Pokemon. More common are 1km (Caterpie), uncommon are 3km (Charmeleon), and rare are 5km (Snorlax). I’ll update this as I learn more.
Here is a list of how far each pokemon has to walk in order to get 1 candy of its kind.
You can change your buddy anytime you want. However, you will lose any progress you have made towards earning candy for your current buddy.