Only when your budgie is tame and happy to perch on your finger inside the cage should you then allow them out of the cage to fly. Once they are at that stage you should let them out for as much as possible so they can get regular exercise so try to give them at least an hour a day of flying time.
You need to adapt your room so that it is escape proof, make sure you close all windows and doors in the room so there is no way out. Draw the curtains, as budgies will usually fly towards the light and do not notice the glass in the window. Budgies will also try to fly through narrow gaps and can easily injure themselves in the process so doors need to be closed not just pulled to.
Your budgies first experience flying outside of the cage will be a memorable moment for you, while the bird may be kept in captivity you are allowing them the freedom to be part of you family and fly around in your home. When you first want to let them out to fly you should let them perch on your finger inside the cage, them slowly lift them out and place them on top of the cage so they get a good view of everything and can decide for themselves if they want to fly or not.
After a while of them being on top of the cage and sussing everything out, they will usually fly off and settle somewhere high up in the room. They could stay there for a long time and be panting quickly as it is a very big adventure for the bird to be coming out of it´s cage for the first time. You should keep talking to your budgie in a soft calm voice as to reassure them that everything is ok and they are safe.
Sometimes the budgerigar will not return to its cage and stay up high where it originally flew when it came out of the cage. To get them back into the cage you can try to lift the cage up to their level so it can clearly see that it is their home. Be prepared though that you may have to wait until hunger kicks in and they return back to the cage in their own time. Never attempt to persuade it to come down to its cage by shooing and waving things at it, this will only confuse and frighten them.
You should do your best to avoid giving any food to your budgie outside of the cage, as they may no think they need to return to the cage to eat. If the budgie does not return to the cage and you need to get them back in then the best way to catch them is to throw a soft cloth, towel or net over them. They will usually keep very still and you can hold them from their back when their wings are down and place them back in the cage.