The Eta Aquarids meteor shower was first isolated (and pinned to an orbital event) in the 1870s, when Lieutenant-Colonel G. L. Tupman observed them while sailing in the Mediterranean Sea. As with many astronomical observations of the era, it was catalogued and annotated; it wasn't until William Herschel corroborated the shower with the recent passing of Haley's Comet (and did an orbital plot) that the shower was tied to Halley's comet in 1876.
When observing meteor showers today as then, you will notice they appear to originate from a hidden point in the sky, this is called a radiant. The radiant for the Eta Aquarids is near the star Eta Aquarius, and varies in inferred size by 5 to 7 degrees depending on celestial mechanics. The meteors streak across the sky from a point in space near the star; tracing the paths they make will take you back to this point of origin.
Due to the Earth's orbit around the Sun, the angle the meteors appear at, shifts by a few degrees each night, moving generally eastward and towards the ecliptic (south in the Northern hemisphere, north for the Southern hemisphere.).
One of the unique aspects of the Eta Aquarids is that they're more readily observable from the Southern hemisphere; this resulted in a paucity of observations from their confirmation until the mid 1920s, when Australian and New Zealand amateur astronomers started tracking them. Most years, the Aquarids peak around the 5th or 6th of May, with roughly 30 meteors per hour showing up at the peak from the southern hemisphere, and roughly half that visible to people north of the Equator. (The reason for this is simply that the part of the sky the meteors radiate from is higher in the sky for the Southern hemisphere.) The predicted peaks are usually 15-20/hr for the Northern Hemisphere and for those of us fortunate enough to be in the Southern Hemisphere up to 35/hour on the morning of the 5th and 6th of May! The activity for 2011 is yet to be mapped.
Most meteor showers are gravel and sand-grain sized specks that are left over from the nucleus of a comet as it passes the Sun. Remember that a comet's tail is always going to point away from the sun, and that's where the "train" of gravel and sand comes from. You can think of the entire ellipsoidal path that Haley's comet makes around the sun as being filled with a streamer of sand and dust, all moving at its orbital velocity; over the course of decades, this orbit and the Earth's change, and eventually the Earth passes through this debris field. When it does, these objects impact the upper atmosphere and burn up.
If you're willing to stay up late (or get up early), this is a naked eye observation event. You'll have best viewing around 3 to 5 AM local time. If you're just getting into the fascinating hobby of watching the night skies, this is a good place to start. The objects are bright, move noticeably across the heavens, and only require your naked eyes to see them. More than a few will leave visible streaks that will linger for a half second or more, making them quite memorable and noticeable. The Eta Aquarids, like their sister shower the Orionids in October (also from Comet Haley), are one of the better annual showers to observe from the Southern Hemisphere, because of where they show up in the sky. In comparison to the Geminids and Leonids, they're much more visible for the Southern hemisphere observer.
If you're worried about getting hit by something from the sky, you should be! However it's not going to be from a meteor shower. The big hazard is earth-crossing asteroids, like Apophis (but that's a story for another day). While the Earth takes on about 14 million tons of meteoric dust in a year, the grand total, when compared to the mass of the Earth's atmosphere, is negligible.
What is potentially interesting is that some say the seeding blocks for life came from meteoric dust; this is part of the theory of "PanSpermia" by Sir Fred Hoyle. While not widely trafficked in astro biological circles, it hasn't been ruled out entirely. Certainly, anything that could survive both the vacuum of space, crossing the Van Allen belts, and survive the thousand degree temperatures of crashing through the atmosphere would be quite durable and would likely out compete anything it found on the ground. On the other hand, it's great fodder for science fiction stories, particularly down here in Australia, where our experiences with invasive species have been so colorful.