Togepi is one of the cutest Pokémon in the series and you'll find one in Pokémon Sword and Shield. Even though he stays cute the entire time you have him, Togepi evolves. It has two evolutions, Togetic and Togekiss.
Before you can think about progressing through Togepi's evolution tree, you must first find one. You can only find them at the Wild Area's Bridge Field location in normal, overcast fog. Even then, the chances of locating any of them are minimal, so you may find yourself wandering around this area for a long time.
Sadly, Togepi doesn't show up in the planetary world and is one of the sharp exclamation marks forcing you to run into the grass.
Fortunately, a quick way to get a Togepi is to talk to a woman west of Hammerlocke. She will be in the left corner where the Rhinoferos and Tritosor are fighting. Talk to her and she's ready to trade a Togepi for a Toxizap. If you can acquire a Toxizap, you can receive Togepi much faster than if you were just looking for it.
When you get your hands on Togepi, you need to develop your friendship with the creature. You have several ways to do this, the easiest being to have it in your main party when traveling in the Galar region. You can also curry him in your camp, provide him with the berries that build friendship, or have him participate in The Pokémon Battles, without passing out. If he passes out, you lose some friendship.
You can check your progress with the Friendship Checker in Hammerlocke. When you have enough friendship, you need to level the level again so that your Togepi becomes Togetic. Togepi starts off as a fairy type, but changes to a fairy and flying type after he becomes Togetic.
Now, to acquire the final evolution, you must use a shining stone on your Togetic. You can find the Shining Stone at only a few places in the Galar region. There's one behind the great stone circle at Outrage Lake, or you can try your luck with the Digging duo to get them to dig it. You can find them in Bridge Field, next to the nursery. It costs 500 Watts for their services.
If you're struggling to get hold of a shiny stone, it's possible that Melofey, Melodelf, and Seleroc are holding one when you capture them. You can farm their respective sites to try your luck at getting a stone this way.
When you have found the stone, give it to your Togetic, it should soon evolve into Togekiss.