If you cherish your personal space, transportation by taxi definitely has the Shanghai Metro and public bus systems beat. They do cost a bit more, starting out at RMB 12 at flag fall during the day and RMB 14 from 11 p.m. to 5 a.m., still cheap by Western standards, but that pricepoint purchases privacy and some air-con (probably).

The question is: how do you tell the cab driver where you want to go? Well, that depends entirely on what part of the Expo you want to visit.

If you don't mind the possibility of an extended walk through the Expo's expansive grounds (it's an over 5 km walk end to end) just tell the driver that you'd like to go to Shanghai Expo:

"Wo yao qu Shanghai Shibo Hui"

If there you have one of the Expo's 13 gates in mind, you'll want to say the name of the cross streets after "Shanghai Shibo rukou" (rukou = entry gate). So for example, to say

"I want to go to the Houtan Lu/Yuanyi Lu Shanghai Expo gate"

it's

"Wo yao qu Houtan Lu/Yuanyi Lu de Shanghai Shibo chukou"

There are thirteen gates leading in and out of the Expo Park:

Five in Pudong; at Houtan Lu/Yuanyi Lu, Changqing Lu/Yaohua Lu, Yaohua Lu/Shangnan Lu, Yuntai Lu/Pudong Nan Lu, and Shibo Dadao/Yilin Lu)

Three in Puxi; at Luban Lu/Longhua Dong Lu, Xizang Nan Lu/Zhongshan Dong Yi Lu, Bansongyuan Lu/Baotun Lu

Four ferry piers entrances on the bank of the Huangpu River; Qichangzhan, Qinhuangdao Lu, Shiliupu, Dongchang Lu

One Metro station; Line 13 Madang station

More about Shanghai Expo 2010 on Chinatravel.net:

Shanghai's Ever-Expanding Subway System: How to Keep Track

Shanghai Expo: Using the city's Expo shuttles and buses

Shanghai Expo: Visit the Expo using the metro

Shanghai Expo: Exploring the city by ferry

Shanghai Expo: your best Shanghai Metro map resource