1. Wait for Inspiration - I would really encourage you not to just start plowing through quests because you feel that you have to. Instead let a moment of boredom, raiding burnout, or nostalgia give you the jump start you need to get started. While there will certainly be grindy and painful moments along the way the experience should be largely enjoyable. If you find you hate it, or dread the thought of working on it, don't. I know many people feel like they need to get this achievement before Cataclysm, but the fact is you don't need to do anything. Its a game, only pursue things you enjoy.
2. Choosing a Zone- There are two good options for where to go first. The first is to go to a starting area that you haven't done. While not the most exciting of areas, staring areas are great because the quests are quick and generally don't send you all over the continent. You can knock out a whole zone in one easy sitting and get the ball rolling. The second idea is to pick a zone that you haven't spent much or any time in while leveling any of your characters. It will give you a sense of adventure and discovery that the achievements are all about. Zones I found that I have barely touched in all my WoW time (alliance side) are; Feralas, The Badlands, The Burning Steppes, Blasted Lands, Searing Gorge, Eastern Plaguelands, Western Plaguelands, Desolace, Azshara, and Silithus.
3. Preparing - Before you set out for a session of questing be prepared. If you look up the zone you are going to on Wowwiki there will be a link to an article just about the quests you will find in that zone. In that article there is often a list of materials that you will need to complete certain quests as some quests require things that are not dropped by the mobs in the area. Its a good idea to hit the AH and pick those up before you go. Cleaning out your bags is another important step. Put extra gear sets, consumables, mats, etc in you bank and vendor any junk. One thing to keep in your bags is your fishing pole, more on that later. Remember to turn on 'track low level quest givers ' on your minimap. Finally make sure your quest log is mostly empty.
4. Questing - I'm sure you know how to quest efficiently. I'll just say two things. First, many old world quests send you all over the world. If you get a quest that requires you to go to some far off place its a good idea to just continue working on the quests you can complete in the zone and then journey to that far off place either at the end of your session or at the beginning of the next. Secondly, and most importantly, READ THE QUESTS! Yes, it will slow you down at bit, but the reward is worth it. These achievements are about learning about and exploring the world. You can't do that without reading the quests. Its fun, I promise, just try it.
5. Profiting - A great bonus of doing these achievements is that they can net you a nice amount of gold. In Outland and Northrend the quest reward gold alone will add up quickly. I heard somewhere that by just completing the Icecrown zone if you combine quest rewards and vendoring the items you receive you can make somewhere around 1,500 -2,000 gold! As far as old world goes the money comes from all of the various crap you will be collecting. If you take the time to loot all of your bodies you will collect a crap ton of old world cloth that you can either sell or save for your Cataclysm alts. If you have an enchanter old world enchanting mats go for quite a nice sum. If you are a skinner, herbalist, or miner prepare to hit the jackpot. Collect any nodes you see and you will find that many of these old world mats go for obscene prices. I sell rugged leather for 50g a stack. Pretty much if an item is of white quality or better check the price on the AH before you vendor it. Things like pearls or old world meat can sell for much more than you think. Additionally, check vendors for any recipes you might be able to sell and if you don't mind a little fishing, some old world fish are quite lucrative. I'd suggest that you have a bank alt set up so that you can mail all of your finds to that toon and continue questing uninterrupted.
6. Understanding the Difference Between Loremaster and The Seeker - Loremaster requires you to complete a certain number of quests in each area whereas The Seeker requires a flat 3000 quests completed. Although the number of quests needed for Loremaster is less than the number needed for the Seeker most people complete the Seeker first. This is because the quests that 'count' towards The Seeker don't always count towards Loremaster. The general rule is this, quests that take place in a dungeon, are a daily quest, or are a holiday quest count for The Seeker but do not count for Loremaster. Daily quests only count towards The Seeker the first time you complete them.
7. Tools - Many people use EveryQuest in combination with LightHeaded to make sure they are getting all of the quests in an area. Personally I haven't installed these yet, although I'm sure I will when it gets down to the nitty gritty of collecting those last few quests. If you like to be very organized and methodical though I'd suggest them. If you haven't already, search through the user interface options and turn on a feature that will put an exclamation point over an item in your bags that starts a quest. Also visiting the Wowhead comments or other like sites can provide great information and encouragement.
8. Being An Achievement Whore - If you are so inclined you can get a mountain of other achievements along the way. I'd encourage you not to get bogged down in this however unless you are really enjoying it. Do it if its convenient or fun, don't do it if its sucking the fun out of the experience for you. I'm not going to link every achievement that you can do along the way because it might make be burst into tears. Instead here are some suggestions for categories of achievements; Exploring Achievements, Fishing Achievements, Cooking Achievements, Reputation Achievements, Classic Dungeon Achievements, Pet Achievements, Loving/Killing Critters, The Key Achievement, The Well Read Achievement, and I'm sure there are more.
Finally remember to stop and smell the virtual roses while taking a screenshot or two before the world is torn asunder in Cataclysm.