Using your smartphone as a webcam is no rocket science. For one thing, your iPhone has a built-in camera with a pretty decent resolution. If you need to do more than just point and shoot, you can use an app like Zoom to stream your video to your PC or Mac. If your smartphone is a bit more old school, you can take a stab at buying an off-brand webcam off of eBay. Alternatively, you could take the high road and visit your local tech shop to see what they have to offer.
Aside from the usual suspects (WiFi, hotspots), there are a few other factors to consider. You want to use a webcam with a decent resolution, preferably one with a touchscreen interface. This will make for a much easier time of it all around. While you're at it, you might as well consider upgrading your aging smartphone to the latest model. A new phone can cost hundreds of dollars and you might as well splurge for something with a bit more juice.
One of the easiest and most effective ways to do this is to use an app like Zoom. Its web interface is a breeze to navigate and it allows you to point your phone's camera at anything you'd like. Alternatively, you can opt for a hardware webcam like the popular Logitech Z60. Zoom is a bit more expensive, but it's a worthwhile investment. You'll be rewarded with better quality images and the ability to stream video to your desktop or laptop.
While the aforementioned app is the obvious choice for most users, there are dozens of free and low-cost options. The trick is to find the right app for you and your smartphone of choice. If you need a more hands-on approach, you could take a trip to your local tech shop for a one-on-one demo. They'll probably be more than happy to oblige. The only snag is that you'll probably have to leave your phone for a bit while they set up your desktop. A good rule of thumb is to let them know you're a busy professional and they'll be more than happy to oblige.