Togepi is one of the cutest Pokémon in the series and you'll find one in Pokémon Sword and Shield. Although he stays cute the whole time you have him, Togepi is evolving. 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 Bridge Field location in the Wild Area during normal, overcast foggy weather. Even then, the chances of locating one of them are slim, so you may find yourself wandering around this area for a long time.
Unfortunately, Togepi doesn't show up in the planetary world and is one of the sharp exclamation marks forcing you to dash through the grass.
Luckily, 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 to the Galar region. You can also feed it curry at your camp, provide it with friendship-boosting berries, or have it participate in Pokémon battles, all without passing it out. If he faints, you lose some friendship.
You can check your progress with the Friendship Checker in Hammerlocke. When you have enough friendship, you need to level up again so that your Togepi becomes Togetic. Togepi starts out as a fairy-type, but changes to 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 in only a few places in the Galar region. There's one behind the large stone circle at Lake of Outrage, 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 having trouble getting a Shiny Stone, it's possible that Clefairy, Clefable, and Séléroc are holding one when you capture them. You can farm their respective sites for a chance to get a stone this way.
When you have found the stone, give it to your Togetic, it should evolve shortly after into Togekiss.