When your head instructor feels that you have acquired all the knowledge and experience for a particular strip or belt, it will be awarded win an informal ceremony typically at the end of class.
For adults, it generally takes 1-2 years to move from white to blue belt. From then on it typically takes 2-3 years per belt. Of course there are exceptions to this. In the end, the decision is up to the professor.
Because children have more belts, they are promoted more often. It generally takes around 9 months for a child to be promoted up from white belt. In most cases, it takes about 1 year for each belt after white. For kids, stripes and belts will be awarded by the instructor of each class.