The tradition dates back to Pre-Hispanic times. When colonizers and missioners arrived into the American continent, they brought religious figures with them. The Mexicas had a similar tradition, as they made amaranth figures of Huitzilopochtli as a child, that they then took to the temple, where they were blessed and then they took them home.
During Candlemas in Mexico, people take their figures to church so they are blessed by the priests but before the event, the figures have been repaired, painted, and dressed up.
Nowadays, you can find people selling these outfits in every market in Mexico City, as well as many workshops and stores in Mexico City's historic center but now there are catalogs to choose from and even online shops.
So if you want to dress up your family's figure, don't forget to stop by any market in the city!