1. Learn to fish (and cook). If you're going to be fishing for the mount, you might as well learn to fish and cook while you do it. The mount itself drops from fishing pools in Northrend, so if all you're doing is going for those, it'll take you a little longer to level than just sitting in Stormwind and leveling fishing (which you can definitely do), but you might as well up your profession while you do it. El's Angling is the guide of choice -- follow it closely and you'll be 450 Fishing/Cooking in no time.
2. Find Fish. If you follow El's guide, you'll figure this out along the line, but even if you've already leveled fishing, you'll definitely want to make sure you've got the Find Fish ability, obtained from the Weather-Beaten Journal, which you get from -- you guessed it -- fishing. This will help you find fish pools on the minimap tracker, and since you need to fish in pools in Northrend to get the mount, it'll be a huge help, if not invaluable.
3. Watch or listen to something. This is more of an out of game tip than an ingame one, but fishing is boring. It's designed to be boring (probably because the real thing is boring, too). You'll have much less chance of going insane while doing all the fishing if you distract yourself a little bit -- turn on a movie, the ballgame, or a podcast or two (ahem) in the background. I like to tweak my UI while I fish as well -- turn your ingame music off, and everything but sound effects down while turning your overall volume up. That'll make sure you hear the splash you need to click, while leaving the rest of the background sound out of it.
4. Choose your fishing spot carefully. Unfortunately, the mount is only found in Northrend pools, so you won't be able to fish in the pools of, say, Terrokar, and try to farm Mr. Pinchy and the Sea Turtle at the same time (though wouldn't that be great?!). But that doesn't mean that there aren't valuable things to fish up while farming the mount -- take a look on the AH and see what kinds of fish (and food, if you have leveled cooking) are selling, and then do your grinding on that stuff. Given that the mount can come from anywhere in Northrend, you have lots of different places to fish from, so check with your guild, too, and see what's needed, and then do your fishing there.
5. It's not going to be easy. Like we said, everything Blizzard has told us about this mount tells us that it's very, very rare, and that the drop rate is very, very low. Blizzard has a habit of raising drop rates later on once a really rare mount has been out for a while (note that's drop mounts, not achievement mounts -- those they usually remove from the game completely), so eventually we're guessing it'll be easier to get. But it's brand new and it's designed to be hard to get, so if you really are going all out trying to get it, prepare to be fishing for a while.
Or who knows -- even with a really low drop rate, there's always that chance you'll pick it up right away. Good luck!