When I worked at a catering company years and years ago (I feel old now) this is how I was taught. I cut so many melons during the summer time that I still to this day could probably do this with my eyes closed. But I won't. Because it's not safe. Duh!
First, you need to pick the best watermelon.
Find one that has a yellow bottom.
The more yellow the better.
It means that it's sat on the ground attatched to
the vine the longest.
Makes for a more ripe and sweet melon.
Next, look like a complete idiot in the grocery store and
start knocking on the melons that have yellow undersides.
If you hear a thunk solid sound, move on to the next.
You want to hear a loud hollow sound.
This ensures that it's juicy and not mealy.
Once you've got it home, grab a large and sharp knife.
Sharp being the most important part.
Cut both ends of the rind off.
This is where I usually have a plastic bag near by or
my garbage can.
The rind will pile up fast once you start cutting.
Next, cut the melon in half so it's easier to work with.
Starting with one half, turn it up on it's side.
With your knife in hand start slicing off the rind downward.
Try to cut off as much as the white part as possible.
Once the rind is off, trim off any excess white parts.
Cut it in half lengthwise.
Slice that half in half (or thirds) lengthwise through the middle.
Cut it 4 or 5 times into strips.
(I turned it in the picture so you could see it better.)
Finally, cut it 5 or 6 times width wise to make cubes.
Repeat steps with remaining watermelon.