How can I know if a Pokemon has reached its final stage of evolution in Pokemon Go?

In Pokemon Go you cannot evolve a Pokemon that is in its final evolution (disregarding mega-evolution from other Pokemon games and anime).

• You know a Pokemon is in its highest evolved state if there is no Evolve button.
• You can learn the total possible levels of evolution in the Pokédex entry. It shows the existence of all evolution levels, (although those not yet seen show up as nameless shadows). This offers more detail than the "main" Pokemon page, as it allows you to see if there are multiple possible evolutions beyond yours, as well as lower-evolved forms.

Here is a table of all the Pokemon evolutions however only Generation 1 and Generation 2 Pokemon (i.e. the first 251 Pokemon of the National Pokedex) are currently available in Pokemon Go.

Basically, if there is no "Evolve" option, then the Pokemon is at it's highest evolution

There are some Pokemon that do not have any evolutions at all, like Pinsir for example. You can see the full list of 1st gen Pokemon here (Pokemon Go currently only has the 1st gen in it's Pokedex)

As the newer generations are released, this also releases new evolutions, and some pre-evolutions for existing gen Pokémon, and with the addition of the new Magnetic, Mossy, and Glacial lures, some specific Pokémon require these in order to evolve, which the option will only appear if you have one of these applied to a nearby PokeStop (E.g. Magneton will only show it's ability to evolve if you are in a Magnetic lure that has been applied to a PokeStop).

And finally, with the new addition of "Mega Evolution", only certain Pokemon have the ability to Mega-Evolve, and (currently) they are still releasing them one by one (at time of posting, only Blastoise, Charizard, Venusaur, Beedrill and Pidgeot can Mega Evolve). This will always appear as an option for these Pokémon, but require Mega Candy in order to evolve.

Aside from there not being an Evolve button in that case, it is also possible to check your Pokédex, which will tell you the evolution chain of your selected Pokémon.

Example: To view the evolution information of Bulbasaur (#1 in Gen I), assuming you caught it:

1. Click on the PokéBall icon
2. Click on the PokéDex icon (top most at time of writing)
3. Click on the Bulbasaur entry
4. Scroll down and you'll see the evolution section which will list 2 more evolutions (based on whether you catch or saw these next evolution stages, they'll be coloured in or not respectively)

Examples:

Pidgeotto here shows it is on the second evolution but has a third possible (Pidgeot). Charmander shows two more evolutions, but neither is a known Pokémon.

Yes, its the highest if there's no "evolve" button. But expect future updates will allow more species to evolve to higher evolution. I see no official reference for this, but Updates are of essential, and common to online games, for further maintenance and game improvement.

An example would be the Magneton, In the arcade games, and the story of Pokemon, it has 2 evolutions. Read http://pokemondb.net/pokedex/magneton

While it only offers the first evolution, it is of most expectancy to allow the next evolution to be offered. Also, other generation pokemon might be added.

There are two ways (that I know of) of knowing this. The first is seeing if it shows EVOLVE under power up if it doesn't than it is fully evolutionised. The second is clicking on the Pokémon in your pokedex and at the bottom there may be "shadows" of its evolutions.