Before You Get Champion Dailies
Pick up [Valiant's Challenge].
Find Squire Danny on the west side of the ring just north of the western tent. Talk to him, beat a Champion. If you feel comfortable, toss in a few charges to the rotation I suggested before.
Turn it in, squee at your Champion achievement and equip your city's "of ____" title if you're exalted with them.
Pick up [A Champion Rises].
Head to the far western tent and speak to the woman who started all this mess. She'll give you the little brat you can now torture (or love) and 10 [Champion's Seal]s. The seals are in your currency tab from now on, not in your bags. The kid is a real pet (thus you can learn him as a spell) and you can ask him to carry your colors, which makes a flag spawn on him. His tabard doesn't change.
Eadric is to your right in the building by daily quest givers. Crok is on the north side of the Colosseum toward the middle of the grounds.
- [Among the Champions] - Defeat 4 Champions.
- [Battle Before the Citadel] - 1 Commander (green), 5 Lieutenants (red), 10 flying things.
- [Battle to the Enemy] - Kill 15 Scourge.
- [Threat from Above] - 2-3 person group quest available after you finish The Black Knight quest chain. Find the elite Chillmaw just west of Aldur'thar in Icecrown, kill him and 3 Bombardiers.
Let's not forget that the Colosseum is still incomplete and we might see more dailies open up once it's finished, much like the Isle of Quel'danis.
Champion Another City
Go back to your faction tent. You'll see quests available from each race to become a Valiant for another city.
Valiant and Champion quests can be done at the same time, as they have a lot of overlapping goals.
If you just finished your 5th day of Valiant quests to hit Champion, don't panic if they don't show up for your new city. Just wait until tomorrow, when they reset.
Goodies, Prices, and Timing
Viktor went over this on his blog, mentioning it will take 255 days to grind your way to ALL the tabards, pets, banners, and mounts.
My suggestion is to find a friend (or husband) willing to do the elite daily with you but who isn't interested in the buyable goods, and convince them (or pay them) to help you get pets. Also use any 80 alts to maximize the grind and gather/sell pets, if you can stand the extra time investment. It's a very good money-making opportunity on the neutral AH once you're done collecting.
For all five pets, you need 200 seals at 5 a day. 40 days.
All six mounts are a comprehensive 750 seals at 5 a day. 150 days.
Still, these are solo grindable and I urge people to go for it. :) There's a lot of money to be made in this particular pet trade, too. Considering how long it takes to grind the pets, players will be looking for any way to minimize time spent, even if it means hemorrhaging gold. Add that to the gold you make from the quests themselves, and you can be very rich indeed.
Take into account, though, that they'll likely add more dailies once the Colosseum is finished, causing pet costs to go down. I plan on taking a risk and selling my first pet on the neutral AH.