Veneers will not damage your teeth but some enamel may need to be removed from the front to make space for veneers. Your dentist will fully examine your teeth and take X-rays beforehand to make sure the teeth underneath are healthy and not decayed so are suitable for veneers to be placed. They will be able to tell you if you are suitable for veneers.
If you are not suitable for veneers, there are alternatives such as composite veneers, bonding, orthodontic or brace treatments, teeth whitening or just teeth contouring. The most important factor is that you are told of all the options with risks and benefits so that you make the right decision