I usually cut it in half (through the equator) and eat it with a spoon but the juices tend to spray everywhere. Is there a better way?
I'd say your best bet is segmenting the grapefruit before trying to eat it.
Here's a good video about it. How to Peel and Segment a Grapefruit
Downside: It's a lot more work, and you still wind up with a juice-covered cutting board that needs to be washed.
Segmenting the grapefruit is likely the least messy way, however, if you like the half a grapefruit thing:
There's something called a 'grapefuit knife', which has a curved, serated blade you can use to loosen the segment before you try to scoop them out with a spoon. You'll end up with a fair bit of liquid left over at the end, but you don't end up spraying juice as you try to dig the segments out with a spoon, it mostly just sits in the bowl created by the 1/2 a grapefruit peel.
There's also 'grapefruit spoons', which have one side with a serated edge on it; I've never used 'em for grapefruit, though, but the serated edge might help to keep down the amount of spray when trying to spoon out bits of grapefruit.
... I should also mention that when I think of 'segment', I'm talking about peeling it (without a knife, except to start it), and then manually pulling apart the segments so they're intact, and might have a little pith still stuck to them. What the chef in the video that bikeboy389 linked to, I've always referred to as 'supreming' or 'cutting supremes'
Grapefruits are one of my favorite fruits, and you can get around the entire process by just tossing the whole fruit in a high quality juicer... then you can drink it and never have to worry about spraying yourself (unless you accidentally spill!)
You can go further by adding other fruits like strawberry or grape and even some vegetables with low acid content (so the fruit will overpower the taste of these) and make yourself a very tasty and healthy beverage.
Maybe this should've been a comment, but oh, well:
Little grapefruit juice jets are in intrinsic part of the half-grapefruit experience. If I'm eating one by myself and reading, then I make sure it's not something I mind getting juice sprayed on. If I'm eating with other people, well, we all half-expect to get sprayed.
Face it: if God (or replace with your appropriate deity) intended us to eat half-grapefruits w/out juice spraying everywhere, he wouldn't have made them so darn tasty and juicy.
The enzyme denaturing of membranes makes it possible to remove the skin and membrane without breaking any segment cells
This requires the fruit skin to be pierced to membrane level. The fruit is then placed in a vacuum pot with an enzyme solution. The vacuum causes the air pockets in the membrane to collapse and then filled with the warm enzyme solution which in time dissolves the membrane
The tricky part is buying a bench top enzyme processor though...