A Minim (Half Note), pictured above, is a note that lasts for 2 beats. Minims are a hollow circular note head with a vertical Stem. A Minim (Half Note) written as a cymbal has an 'x' inside of the hollow circle. 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 an x above the top line, it will mean 'play a h'.
Because a Minim lasts two beats, we only get two of them in a bar (each one filling half a bar, hence the name 'half note'). So to count we would generally use the crotchet counting of '1 2 3 4' but only play on beats 1 and 3.
With Minims being so much slower, there isn't really any need for a preferred sticking. Hitting with your stronger hand is usually best though.
The example below shows a bar of music made up entirely of Minims. Counting is given underneath the bar.
The Stem of a Minim 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 Minim with the stem pointing down.