Often, if you're calling someone's phone and it rings only once then goes to voicemail or gives you a message saying something like "the person you have called is unavailable right now," that's a sign the phone is off or in an area with no service. That's not entirely conclusive, though. Someone could also have set up the phone to block you in particular or to send all calls directly to voicemail.
Phone Rings Once Then Disconnects
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Often when a phone is turned off or a cellphone network is unable to reach it for some other reason, like remote location with no reception, the phone will ring only briefly. If this is the case, you can still leave the person you're calling a voicemail or send a text, which he'll receive when the phone is back on or has reception.
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In some cases, a phone may go directly to voicemail if someone else is in the process of calling it. Some telemarketers and others exploit this to leave voicemails while only ringing the phone briefly or not even calling it long enough for it to audibly ring. If you see this happening on your phone, this may be the explanation.
User Busy on iPhone
If someone is busy or on the phone on an iPhone or Android phone, he might set up the settings to mute incoming calls. They may also manually reject incoming calls which, if done quickly enough, can be hard to tell from an automated rejection if the phone is off.
Another tactic used to definitively reject calls in an environment where people don't want their phones to ring, such as movies, doctor's offices or business meetings, is to place the phone in airplane mode. This disconnects the phone from the cellular network and is essentially indistinguishable from the device being off, though technically it remains on. Many phones can use Wi-Fi while in airplane mode, letting them continue to check email and other online services.
Blocking Callers
It's often possible to block particular callers on a smart phone or even have a cellular carrier block calls and texts from certain numbers. To someone who's calling, it can be hard to distinguish this from the phone simply being off or out of service.
One way to tell the difference is to call a phone you can't reach from another number, such as a friend's phone or a throwaway number. Of course, if the person you're trying to reach sincerely doesn't want to speak to you, this might be seen as intrusive.