For the majority of short local cycling trips there is generally no need to wear special clothing any more than you would to go for a walk. Some suggestions however:
There are various types of shoes for different types of cycling but in the very basic sense shoes that are suitable for walking are also suitable for cycling. Other types of shoes worn by cyclists are determined by the type of pedal being used. So SPD pedals require SPD shoes for example.
If you ride at night or in heavy traffic its important to make yourself as visible as possible to other road users. A reflective vest or jacket is ideal and reflective bands for ankles and sleeves are also good to get you seen.
Wet weather gear
Don’t let the wet weather stop you from cycling. All you need is a waterproof jacket and trousers plus some reflective gear.
Keeping out the cold
Wear gloves to keep the cold away and ear muffs can be handy and dress up warmly.