Years of amateur astronomy taught me a few basic methods, all precise enough to work for casual observation. I use this for pointing out common objects, the ISS, Iridium flares, etc. This will work for anything.
1) In simple terms, the zenith represents the point directly above you. That's 90 degrees from the horizon. You can therefore easily approximate, since the horizon is 0 degrees.
2) Most fists, when held out in front of you, represent about 10 degrees. 3 fists = 30 degrees, so start from the horizon and there you go.
3) If an object specified an azimuth, you can calculate by finding north. In the northern hemisphere, north is most closely recognized by Polaris. Find Polaris and that represents 0 degrees azimuth. Directly behind you is therefore 180 degrees. If someone says you need to find an object at 30 degrees altitude and 90 degrees azimuth, that's approximately to your immediate right if you're facing north and up 30 degrees from the horizon.
Again, this only works for naked-eye observation; anything requiring a telescope of course requires more precise calculation, but it's also easier to calculate that way.