You can ride bike in trainers or other regular shoes, but you'll be more comfortable in specific cycling shoes, and they don't have to cost a fortune.
Cycling shoes have stiff soles, so the pedals don't dig into your feet, and usually have mounting points for the cleat from a clipless pedal system so you're securely joined to the pedals.
You can still walk in some cycling shoes — look out for 'SPD' shoes and pedals, which have the cleat recessed into the sole — but road cycling shoes with the cleat on the outside of the sole are awkward to walk in.
Road.cc articles on shoes
Best cheap cycling shoes
Beginner's guide to cycling shoes — the secrets of comfy feet
Buyer's Guide to Cycling Shoes
The best cycling overshoes — what to look for and 12 great choices
The best performance road cycling shoes