Step One is to leave your Herb Picker near a trainer in Stormwind (Orgrimmar). Learn Zen Herbalism as soon as you log in. Also, be sure you have a +10 Herbalism bonus of some kind, you'll need it. The starter quest for Pandaria is a pop-up that triggers when you enter the city. It may not be functioning well when mass players hit the servers. If for some reason you don't get it, just go into Stormwind Keep (Grommash Hold) and that should also activate the quest chain. Then grab the next quest and hop on the flying boat to Pandaria. Once you zone in, leap off the boat (try to hit the water below) and just hoof it to Valley of the Four Winds. You want to get to the middle of the Jade Forest, along the western border. Just follow the western road north as I've shown on this map:
This is where you should be able to find lots of green tea leaf, as well as silkweed near the water. I don't recommend staying in the Jade Forest as the herb nodes there aren't quite as plentiful when lots of players are questing through. If for some reason you have too many folks infringing on you in the Heartland, travel a bit further west to the second yellow area. This section also has decent herbs and few if any players hang out here. You can collect green tea leaf on the outskirts of Paoquan Hollow and up around the plateau east of it. Hopefully one of these two locations will be workable for you.
Green Tea Leaf starts out yellow to you at first and quickly changes to green around 530. You need to reach 545 (535 with buffs) to pick Silkweed, so you'll have to keep picking tea leaf a bit past the change to green difficulty. Alternately you can postpone your trip to Pandaria and pick Twilight Jasmine in Twilight Highlands to skip green tea leaf completely. At 535 you should switch to the northern and western portions of the Heartland area and focus on silkweed. Another area you can go to for silkweed is the river to the south, there are nodes along that as well. Water walking potions could be helpful here if you want to ride down the middle of the river and avoid the mobs on the sides.
Silkweed will change to yellow around 560, but keep farming it until you reach 565. At that point you can switch to Kun-lai Summit and pick Snow Lily (575 without buffs). To reach Kunlai you need to go back to the eastern side of the zone at the spot called the Grassy Cline. This is roughly north of the "T" in Thunderfoot on the second map.
Right next to the flight master at the Grassy Cline is a footpath that leads up into the hills. This turns into a set of stairs that take you up and into Kunlai. Follow the stairs, then the gravel path (stay on the lower portion after you pass the Tavern) and keep going until you reach the river. Stay on the west bank of the river and ride into the tunnel. Hug the left wall of the tunnel to avoid aggro from the level 90 mobs in here. Usually they don't attack if you're careful, but you can lose them at Kunlai if they do decide to jump you.
Once you pass out of the tunnel, you will be at Binan Village in Kunlai Summit. Follow the road towards One Keg as I've marked it on this map:
In this zone I would advise you to stay on the road and try to dodge any mobs that wander near the road if you can. From One Keg head west past Kota Basecamp and then swing north towards Winter's Blossom. I would be wary of stopping for herbs along these roads as the aggro can be swift and brutal. Just before you get to the camp at Winter's Blossom, you'll reach a fork in the road - take the northeast fork. Ride through the camp and up into the mountains. (A shortcut into the mountains that may save a few minutes on your time is to ride directly west from One Keg. Run straight up the mountainside and onto the Burlap trail. There may be elite, aggressive mobs here, so run past and hope you can shake them. Follow the flags up the mountain until you reach the actual trail).
Once you make it into the mountains past Winter's Blossom, you should start seeing snow lily nodes on your mini-map. There aren't a ton of herbs in this area, but there should be enough for 1-2 people to farm without too much trouble. The main attraction with this area is that it's easy to avoid aggro from the nearby mobs. There are some non-aggressive goats, as well as cats and yetis. Aggressive mobs can be ignored if you give them a wide berth. There are also a couple of quests that pass through here, but those mobs can also be avoided if you keep your distance. Feel free to explore all the various nooks and crannies for herbs as the paths through here aren't well marked on the map.
It will likely take about 20-25 minutes of gathering in Valley of the Four Winds, plus another 20 minutes or so in Kunlai to reach the new Herbalism skill cap (600). For the record I found one golden lotus while I was farming snow lily, if that gives any indication of it's rarity. Kunlai is marked as an 87-88 zone on the in-game map.
I took notes while collecting herbs and they mostly follow this difficulty chart:
Green Tea Leaf = Requires 500 | Green @ 530
Rain Poppy = Requires 525
Silkweed = Requires 545 | Yellow @ 560
Golden Lotus = Requires 550
Snow Lily = Requires 575 | Yellow @ 590
Sha-Touched Herb = Requires 575
Fool's Cap = Requires 600
I don't have good notes on some of these herbs because there just wasn't enough of them around for me to track the changing difficulty levels. I will make updates to this list on my second pass if I'm able to get better information. The herb requirements are all accurate as of the current build except for Golden Lotus. I wasn't able to find one to check it, so that number is from an older version of my notes.
9/6/2012 Update: I leveled Herbalism for a second time today and most of this information is still relevant. I refined some of the herbalism numbers and changed the run times according to my second test. I'm still recommending the same basic leveling process. The elite mobs near One Keg may have been removed/phased, so that route up the mountain looks more promising now.
Feel free to post any questions or concerns in the Comments and I'll add them to my notes for the next round of testing :)