It's best to approach your tortoise so it can see you, head-on. Make sure it's on a flat surface, with no way of falling off (its cage or the floor is best). Pet its head, avoiding its eyes. If it lets you do this, try rubbing its cheeks and under its chin. Tortoises can also feel through their shells, so pet yours on its back with your fingers, running them back and forth along their shell or making circular motions.