It is quite safe to let your bird out for a fly around the house from time to time, as long as you use your common sense to keep it safe. Before opening the cage, close the windows and doors, protect open fireplaces (even if there is no fire), cover up any houseplants and, most importantly, put the cat and dog out! It is also a good idea to close the curtains and cover up any clear glass to prevent your bird from flying into windows. If you do let your bird out for a fly around the house, make sure you collect and dispose of any droppings and keep it away from food preparation and eating areas.
Catching your bird
Letting your bird out for a while may be a good idea, but it may be so excited to have an opportunity to explore (and so unused to the feeling), that you may have trouble recapturing it when it is time to settle down! If this happens and you have exhausted your efforts, try this method as a last resort. Darken the room, drawing the curtains if necessary, and locate your bird by the light of a torch. Quietly walk up to your little renegade and use a soft hat or something similar to recapture it. Gently hold your bird, placing one hand around the body and wings, with your thumb and forefinger at each side of its head. In time, most birds will learn to return to their cages on their own.