Catching them is hard, even if you’re experienced and the bird is used to you. He’ll likely try to fly off with the sparrows if he’s hanging around with them, if you approach. But, just try to go slowly and not spook it. My mom caught a loose parrot in her yard with an old shirt thrown over it, but it all depends on how tired they are and how spooked they get. Some budgie calls played on a tablet or cell phone might entice it to come closer during the day if it stays away from you.
If you do catch him – you can offer fresh foods (no avocado, onion.. the stuff the buns eat is fine though), seed and water. And check places like 911 parrot alert (website), craigslist and vets in the local area (50ish mile radius) to see if anyones looking for a lost budgie. If you plan to keep him, you’ll want a cage (my advice is order online, in pet stores they sell TINY cages that are way over priced and too small for budgies to fly in) and good seed brands are volkmans, dr harveys, ecotrition is OK for pet store brands (I buy organic blend sometimes). Something that isn’t 90% white millet and has a variety of seeds.
Signs of illness to look out for are lethargy, staying puffed up and near the bottom of the cage, poor feather quality and off-color poop. There are websites dedicated to poopology (lol) to see healthy birds poop, I won’t gross people out by posting any pics. Generally, under stress their droppings can get a little watery and exact color varies (from tan to green and even red if it’s been eating dyed foods) but the urate (white spot) should be white no matter. A vet checkup would be a good idea if you plan to keep it, since it’s been out in the wild. There are a few things they can cross-transmit (though not horribly common and often fatal to the birds), so follow good hygiene until you know its health status.