How Do You Know If A Coin Is Proof Or Not

What year is this coin?

To answer your title question: by studying the minting process. Sorry for being so blunt.
John1

Well this ones not a proof coin. Typical business strike. Hiding the date/mintmark on purpose. I'm guessing the is a pre 1980 Philly coin someone is trying to pass off as a missing mintmark coin. But it a normal dime from Philly. So to play your game.

Note the rims on the Business strike and the proof dimes. Note the rims are stronger on the Proof coins? Proof coins are struck twice. So the rims look stronger. (They may use different collars also, but don't quote me on that) Strike a lot strong. (Proof dies are used to strike 3,000 coins. (6,000 strikes) So the fields are mirror like. Your coin is showing all evidence off being a normal business strike.

For the modern collector Proofs have polished fields and cameo devices.

I like to collect proofs that were made before the time that Mints around the World started to market proof coins in their millions, for large scale profit.

These sorts of proofs, for the most part, do not have polished fields and cameo devices. They are identified by sharpness of detail to the extent that the difference between circulation coins and the proof equivalent is still reasonably obvious. Needless to say, such proof coins over 100 years old should be collected in 'as struck condition. All of them are very rare.
Also needless to say, I have less than five of such coins in my collection.

British proof sets of the 1800's are a good example.