I start my sweet potatoes in jars on the window sill. I've seen other ways, but this takes very little counter space and works just great.
I just shove sweet potatoes into jars, pointed side down, with part of it sticking out of the top of the jar. If you can find potatoes with pink bumps already visible, then use those - they'll sprout faster from the top. Leave the pink bumps at the top, out of the water.
In time, little pink sprouts pop up from the top and white roots show up under the water.
In a couple of weeks, or when things get really warm, the sprouts will grow pretty quickly, and leaves will open up.
If you can find a jar deep enough, just put the whole potato in deeper so the sprouts are under water, then they'll form roots at the base of each sprout.
If you don't have really deep jars, don't worry. Carefully twist the starts off the potato when they're a few inches tall and have a leaf open.
Then put the sprouts in a water in a jar. Soon they'll develop roots on their own.
Easy squeezy!
Once you see roots, you can plant them. Make sure you are well past the last frost date for your area. Sweet potatoes like warm soil and hot weather.