Arrive in Kathmandu, Nepal. Round-trip, economy flights from New York to Kathmandu typically cost between $2,000 and $2,500, depending on the carrier and the time of year. A cheaper option would be to fly to Delhi, India (for around $1,000) and then take trains and buses to the Nepali capital for another $150 or so.
Find a guide service in Thamel Market, Kathmandu. Thamel is filled with licensed guides, mostly for Nepal trekking trips but also for Tibet trips. This is important, since to visit "China," one must visit with a group--this is the only way to secure a Tibet Travel Permit. The guide services in Thamel can help you obtain this. Usually, a Tibet trip will cost between $500 and $1,200.
Drive to Pokhari, a Nepalese border town. Your guide will set you up with a bus or jeep that takes you there, along with any other member of your "group" (often just one other person). The ride takes the better part of a morning, and by the end you'll arrive at the border, looking across the Friendship Bridge to the Tibetan town of Dram on the other side.
Enter Dram. To do so, you'll have to cross the Friendship Bridge on foot, then show your papers (given to you by the travel service in Kathmandu) to the Chinese guards on the Tibetan side. They'll stamp them, as well as your passport, and you're in!
Drive from Dram to Lhasa. This usually takes several days, as you'll be heading up and over the Himalayas (with views of Everest and several other incredibly tall peaks), through a number of towns and villages, and across the Tibetan Plateau. Your guide service will have arranged for all of your transportation and accommodation from Dram to Lhasa.
Enjoy Lhasa. Don't miss the Potala, of course, but the Barkhor (including the Jokhang), hugged by the Tibetan ghetto, is also worth some considerable time, not to mention Sera and Drepung monasteries. If you have time, catch a bus out to Ganden monastery as well--possibly the most picturesque of all Lhasa attractions.
Fly from Lhasa to Kathmandu. Your travel guide from Kathmandu will have arranged for your flight.
