*With* Eyes of Ender

Yes, you throw an Eye of Ender to find the stronghold. This can be easily found with a quick Google search.

And an answer on Arqade.

As of 1.9-pre4, you can use Eyes of Ender to locate the direction of a stronghold by throwing them up in the air. Once thrown, they'll change direction to point to the stronghold.

The above is still how it's done, despite the fact that it was done for 1.9-pre4.

It is better to have more than one Eye of Ender, as they are easily lost wasting your time, but it will come to a point where the Eyes keep going to a single point on the ground. This point is where the stronghold lies. Dig down and you shall find.

*Without* Eyes of Ender

Not to offend, but choosing to do such a thing, is highly unlikely to fetch results, and is even more likely to take a lifetime, but there are multiple ways to achieve this.

Exploration Method

The "Exploration Method" solemly relies on your abilities to scan your world from top to bottom, by searching for an entrance. The thing is however, Strongholds don't have an entrance, so the "Exploration Method" only really works for underground caves and systems which may lead into the Stronghold itself.

Map Method

Another alternative to this, is to use a map viewer, and look around for anything "Stronghold" suspicious. Here is another extract from the brilliant answer on Arqade.

There is no in-game way to find a stronghold, but you can use a cartography program like MCMap Live (Mac) or Cartograph G (Windows) (see also this question for other alternatives) to look for tell-tale signs of a stronghold: iron bars and bookshelves.

Here is an image from the answer showing an example of what to look for (Enhanced):

Good luck!

To clarify. When it is said to throw.. they don't mean pressing q. (Or circle or b on consols) but to activate using right click (or left trigger on consol)

If you are trying to get achievements make a copy of your world and activate cheats in the copy. From there use the /locate command an example is (/locate endcity ) <-- so then remember or copy the coordinates and just go to them in the original world and this works with anything. This is a easy way to find any location in Minecraft!