If you have another budgie (or could borrow one), secure all the doors and openings to its cage with twist ties and put the cage outside. The caged bird’s chirps will almost assuredly attract the loose bird if it is nearby. Then put an empty cage right next to it, up against it, with the door propped open. Put some seed and water inside, the seed spread visibly on the floor. Rig the door with a string (tied to a stick that props it up or something) so that it can be pulled close if he ventures in. Try hiding around a corner or behind a door so as to not scare the bird off. If the budgie you’ve caught is someone else’s lost pet, the right thing to do is try to find the owner. Try putting a found ad in local newspapers and ad booklets. (Found ads are usually free.)
How Do I Catch a Loose Budgie?