Use a towel. If the budgie is perched on a high surface, such as a curtain rod or a bookshelf, you can use a towel to gently nudge it back into its cage. To do this, hold the towel in one hand and slowly reach out and cover the budgie with the towel. Then, gently guide the budgie back into its cage.
Use a stick or perch. If the budgie is perched on a low surface, you can use a stick or perch to guide it back into its cage. To do this, hold the stick or perch in front of the budgie and slowly move it toward the cage. The budgie will eventually hop onto the stick or perch, which you can then use to guide it back into the cage.
Wait for the budgie to come back on its own. If the budgie is flying around the room, you can try simply waiting for it to return to its cage on its own. If the budgie has spent some time out of its cage, it should be relatively easy to coax back in.
However, if you have tried all of the above methods and your budgie still refuses to return to its cage, it may be best to consult a veterinarian or a qualified avian behaviorist for help.