A Quaver (Eighth Note), pictured above, is a note that lasts for 1/2 a beat. Quavers are a solid circular note head with a vertical Stem that has a 'Tail' coming out of the top. A Quaver written as a cymbal has an 'x' instead of the 'blob'. It is where the note head is positioned on the stave that tells us which part of the kit is played. So if the note head is in the very top gap, it will mean 'play a high tom'.
For counting we will compare to the Crotchet, which we counted '1 2 3 4'. We said we could fit four crotchets into a bar, and the four counts represent each beat in the bar. So if a Quaver lasts 1/2 a beat, logically we can fit twice as many into a bar. Which means we get 8 Quavers in bar. We still want those four beats represented when we count a quaver but we need 2 counts to each beat. To achieve this we add an 'and' count after each number. So we get '1 and 2 and 3 and 4 and'. This is a bit bulky when written down so we abbreviate 'and' to '+'. Giving us '1 + 2 + 3 + 4 +'.
With sticking there are 2 options. When used in a groove you will usually play them all on the right hand. When playing a pattern on (for example) the snare, we will usually alternate between right and left. The logic here is that your strong hand (your right hand if right handed, reversed if left handed) plays all the notes 'on the beat', so the '1 2 3 4' and your weak hand fills in the notes 'off the beat' (the '+' counts).
The example below shows a bar of music made up entirely of Quavers. Counting and is given underneath the bar.
The Stem of a Quaver may be positioned coming up from the note head or coming down depending on it's vertical position in the stave. When it goes up, it will be on the right of the note head. When it goes down it will be on the left. The image below shows a Quaver with the stem pointing down.
When we get 2 or more Quavers in a row a 'beam is put over the top. In our standard bar of 4/4 quavers are beamed when there is a group of 2 or 4. The images below show how these look.