As a longtime player in World of Warcraft, the quest chain starts in the building to the west of the Crusaders' Coliseum. Justicar Mariel Trueheart directs questers to their faction's respective tents on the east side of the keep, where they must undertake a series of tests to join the tournament proper.
Also remember that like the fishing and cooking daily quests, the 3 blade quests (A Blade Fit of a Champion, The Edge of Winter, A Worthy Weapon) are not independent daily quests. You should not complete one of them on the day you accept it, you will not be able to do either of the other two quests the following day. In other words, having one of them in your log prevents you from accepting the other two, should it be offered that day. This means that you should do all three daily quests on the day you accept them if you want to complete "Up To The Challenge" in three days.
Over the course of championing all five faction's cities you can expect to gain 11,250 reputation with each capital city in World of Warcraft. Keep this in mind when considering champion-level quest rewards. The [Champion's Writ] can only be used to buy reputation tokens worth 250 reputation with one city at a time. Do not purchase reputation with a faction when you can reasonably expect to reach exalted status while doing the valiant chain for the rest of the cities. The [Champion's Purse] is a better alternative for players who already have high reputation with their faction's cities.