The processions start on Domingo de Ramos (Palm Sunday this year is the 20th of March) and all are organized by the local Catholic Brotherhoods, and may involve several hours of hot sweaty walking through the city streets until the icon returns to its church at which point a party may start that lasts longer than the actual procession.
Women are often dressed in the finest outfits or in complete mourning black, children in communion dress, and men wearing robes with tall pointy hats unless they´re helping to carry the icon. Many will be carrying banners, or holding tall candles. In total there are 14 processions taking place in Ronda over 8 days.
Have a look at the promotional video for Semana Santa 2016…
Here is a PDF document (in Spanish) showing all the processions and times. semana santa 2016