Limits are for the weak
You can't just carry any arbitrary amount of gold with you when you move realms. I won't speculate about why, but the limits are set per level, available at the Blizzard support page. If you're over level 80, you can bring 50,000g. I suppose for the vast majority of players, that's fine; however, it doesn't take much work to end up with many times more that. As was mentioned in the email, one recent work-around was introduced recently: The only limit on the amount of gold a transferred guild can bring is the guild gold cap -- 1 million gold.
On the plus side, if you have a character that's been the GM of a guild for the required seven days, moving a guild includes a realm transfer for the GM. It costs $10 more to move a guild with you, letting you move as much gold as the majority of people would ever be able to. It also gives you a huge amount of storage room you can use to store items for arbitrage. If you possess the right leverage on your source realm, this alone might be worth the money and trouble.
The risks of arbitrage
Buy stuff cheap on your source realm that sells for more on your destination realm. It seems simple, and it is -- well, mostly. You have several walls you can bump into, depending on your setup, and you want to try and pick as good a mix of goods as you can.
If you find something that's worth 10 times as much where you're going but you only have room for 500 gold's worth of it, you're only making 5,000g (not to mention leaving a lot behind). If you find something for 100k gold that you can sell for 200k; however, it takes three months. You might find yourself doing dailies until it sells (or worse, taking a loss).
Figuring gold per inventory slot
The more densely you can pack your goods before you leave, the more money you can bring with you. The less money you're trying to move, the less you have to worry about this, but if you elect to pay the extra $10 and simply move a guild, you'll have that much more head room.
Each character has a bank with 26 slots in it and room for seven additional bags of any size or type. There are also a 16-slot backpack and another four bag slots on the actual character. The more you invest in bags, the more room you'll have; however, the profit per slot has to justify the price of the slots. This goes for guild bank tabs, too; they're only cheap for the first few. After a point, they become too expensive to justify unless you're still facing the potential of having to leave money behind.
Divide the amount of money you want to turn into stock by the number of inventory slots you have to save it. Factor in any gear or personal items you'll need to bring, and that number is your gold per inventory slot.
What's your profitability?
Once you've figured out how dense you need to make your goods, you know what kind of goods you can fit so you can start focusing on maximizing your gold on the destination realm. If you're only going to be able to make it using chopper parts and Vials of the Sands, your options are limited unless you can move more than one character or somehow increase the number of slots available to you.
Profitability is the measure of how much more you can sell something for on the destination realm, but can't simply be measured as "lowest price on their Auction House now minus lowest price on my Auction House right now". First of all, obviously, you will have to pay 5% when you actually make a sale. Secondly, you might have to relist something a bunch of times to sell it, and that money doesn't come back. Thirdly, if you bring enough of something, you might well sell your last one for a whole lot less than your first one. You can sometimes mitigate this by selling it a whole lot later than your first one, but then you're exposing yourself to price changes. Also, one of the most dense and sometimes profitable items to bring, BOE gear, only generally goes down in price.
You have to strike a balance between the destination's demand, your original realm's supply, and your raw profit margins to make this work.
A blend of liquidity
Items that you can sell quickly include gear, trade goods, pets, and all sorts of other things. Items you might have to wait on to get a good price are really mounts or vanity items, as well as some trading card loot. Try and make a good blend of items that will sell immediately so you have folding money, as well as some high ticket items that will serve to add density to your haul, even if they take longer to sell.
Generally, you want to try to stick to items that won't become obsolete or increase in supply over time. Two good examples of this are the items from the Shadowmourne quest and rare mounts from critters that won't be killed by many people in the next expansion.
Never skip the research
I don't know what I used to do without the Undermine Journal. Needless to say, being able to see the historical prices for any good in the Auction House on both realms is going to save you a lot of time. You can also use it to research the biggest players on the destination Auction House who might be willing to commit to buying certain items in bulk direct, saving you the time it would take to sell them on the AH, as well as the 5% AH fee.
To make these searches even more trivial, visiting a category/realm page on the Undermine Journal (like this one for pets on Drenden Alliance) will allow you to select another realm from a dropdown that lets you compare prices side by side across the entire category. The categories can be found by hovering over enhancements or consumables on the menu bar.
Maximize your profits with more advice from Gold Capped. Do you have questions about selling, reselling, and building your financial empire on the auction house? Fox and Basil are taking your questions at firstname.lastname@example.org and email@example.com.