You'll usually start your career by going to a model agency in person or sending photographs and details of your measurements to them.
You'll need a good appearance and the right 'look' for the area of modelling you want to go into.
You should usually be well-proportioned for fashion modelling, with regular features and healthy skin, teeth and hair. For other types of modelling you would need to fit in with the look that modelling agencies want.
You don't need to do a modelling course or have an expensive portfolio of pictures. The British Fashion Model Agents Association has advice on what to expect from reputable agencies and how to avoid rogue ones.