You can downgrade your emblems on a 1:1 ratio. So, if you had one Frost, you could downgrade it to a Triumph. If you chose, you could then downgrade that to Conquest, and so on. This is handy if you happen to get a couple of emblems from a higher tier, and you know that because you don't normally get the chance to acquire them, it would take you too long to save up enough to buy anything. Unfortunately, you can't upgrade your emblems.
Tip: Check out our guide to making gold with the new Random Dungeon Tool, since you should be using it to collect emblems!
Now that you've had a quick crash-course in emblems, let's look at some ways that you can use them to make some gold.
Primordial Saronite: 23 Frost Emblems
If you do not currently raid Icecrown, you will have enough emblems to purchase 1 Primordial Saronite in 12 days of doing only one heroic dungeon per day using the Random tool. Wowhead estimates that each one is typically bought out on the Auction House at 2600g; that's not bad for 12 days worth of work! Considering many heroics can be done in under 30 minutes, even someone who can't devote a lot of time to playing can manage this, especially if you queue as a tank or healer.
If you do raid Icecrown, you will have access to Primordial Saronite much more quickly, although you may need to devote some of those emblems to gearing up instead.
As a point of comparison, these tend to sell on my server from 2200 to about 2500g each.
Crusader Orb: 15 Emblems of Triumph
Wowhead estimates that these are bought out on the Auction House for about 125g each. Considering how easy it is to farm these now, you should have easy access to an abundant and renewable supply of Triumph Emblems.
As a point of interest, on my server, Crusader Orbs currently sell for about 250g.
Runed Orb: 18 Emblems of Conquest
You may not want to downgrade your badges in order to pick this up. It will cost more badges than the Crusader Orb, and may be worth less on many servers. However, if you happen to have a stash, why not blow it on these? Wowhead estimates an Auction Buyout price of 150g each. On my server, as a comparison, they sell for about 175-195g each.
By looking only at the Wowhead estimates, one would conclude that Runed Orbs actually sell better, although it is worth noting that both essentially sell for 8g 33s 33c per emblem. It is also important to note that on my server, as an example, the Runed Orbs really do sell for significantly less - 50+ gold less! Do note that this will vary by server for many reasons, and if your Crusader Orb market is saturated, you might make more money selling these.
Epic Gems: 20 Emblems of Heroism for the primary colors, and 10 Emblems of Heroism for the secondary colors
Red, blue and yellow gems will give you pure stats, and so they tend to be worth more. In this case, they are worth twice as many badges as their mix-it-up counterparts!
Red gems (currently, Cardinal Ruby) tend to sell for the most. However, this is a well-known fact, which makes it vulnerable to market saturation. If too many people are trying to make coin with this color, your best bet may actually be to choose another.
In order to figure out the best deal, watch the prices of the epic gems and make a list of the prices each seem to sell for on your server. Then, divide by 20 for primary colors and 10 for secondary colors. The number you get will show you how much gold you are getting per emblem. This should help you decide what to buy!