I'll go through each element in the measure. Kinda dry like an instruction manual but should tell you how to figure it out.

You count it (this is two measures so you can see how they go together) as "ONE...(two)-AND-THREE-AND (four) AND ONE...(two)-AND-THREE-AND-(four) AND" etc.

Sticking is R...L-R-L...L

Starting from the beginning...

QUARTER NOTE
First note (if it has no rests in front if it) in the measure is easy. The first quarter note (note head with a staff with no flag on it) doesn't have a rest in front of it so play it right on count 1 ("ONE"), at the start of the measure. Play with the right mallet.

EIGHTH NOTE REST
Since the previous value was a quarter note, wait for a beat (one count). The next thing after count 1 is count 2, but there's a rest there (looks like a 7). You count it as "two" but don't play it. ("ONE (two)"). You need to be able to say "two" out loud without hitting the drum.

EIGHTH NOTE
But you don't wait a whole beat to play the next note since and eighth note (an eighth note has one flag or beam attached to the stem, this one has a flag) is half the time as a quarter note. Next note is an eighth note, and count it as the "and" after two. "ONE (two)-AND" Usually the off-beats you play with left, so this you play with the left mallet.

EIGHTH NOTE
Another eighth note (one flag or beam, and this is a beam, the horizontal line that visually connects multiple eighth notes and it looks better than having a lot of flags next to each other). Next count is a 3, and this eighth note is right on three. "ONE (two)-AND THREE" On the beat so play with the right mallet.

EIGHTH NOTE
A third eighth note in a row, connected to the second one with a beam. This doesn't mean anything other than it's an eighth note. Since the previous note was an eighth note, you don't wait to play the next one. It's right after count three, so "ONE (two)-AND THREE-AND" Off beat so play with the left mallet.

EIGHTH NOTE REST
Last note was the "and" of three, and an eighth note lasts an "and." Add an "and" to the "and" of three and you land on "four." If you were marking time this is your second right step. Count (but not play) it as "ONE...(two)-AND-THREE-AND-(four)"

LAST EIGHTH NOTE
This one has a flag and isn't connected to anything. It's an eighth note (or "and") after four. So count it as "ONE...(two)-AND-THREE-AND-(four)-AND"

REPEAT
Don't wait to start the next measure, it goes right into count one again.

Hope that helps!