What should I expect in Shanghai?

This is an incredibly broad question, and one that very much depends on where you come from, and what your preconceptions of living in Shanghai are.

In general, westerners coming to Shanghai suffer from a certain degree of culture shock at first, given that the Chinese culture, language, and way of life are all markedly different from most western countries. People interact differently: for example, in China it is not considered rude to inquire about somebody's marital status or salary, or bluntly comment on their weight - even though such things are considered taboo subjects in most western countries. Chinese business practices are often very different from those of western companies: for example, western businesses favour clear, direct communication; Chinese companies are often indirect and subtle when giving feedback, in case negative feedback harms 关系 - guānxì, "relationships" or results in a loss of 面子 - miànzi, "face"/"reputation", both of which are very important concepts in Chinese culture.

Shanghai and the rest of China
It should be noted that Shanghai is in many ways very different from the rest of China. Shanghai is China's expression of the new age, with plenty of modern architecture and technology quickly overcoming the traditional. Many of the places marketed as 'traditional' (e.g. Jing'An Temple (静安寺 - jìng'ān sì), Yu Yuan Gardens (御园 - yùyuán) and Tianzifang (田子坊 - tiánzifang)) are merely simulations of traditional Chinese culture, designed to attract tourists rather than to preserve the culture itself. While places like this are worth visiting for interest value, you shouldn't expect much in the way of authentic, traditional Chinese culture.

Shanghai is without question China's most modern city, and while it may be more convenient living in Shanghai than other towns and cities in China, some feel that the lack of cultural conservation makes the city somewhat sterile; even though most people living here feel that many areas of the city still have plenty of character - at least in Puxi.

Compared with the rest of China, Shanghai is extremely westernised. English is not ubiquitous but is certainly prevalent around the city: street signs and the entire metro system are in both Chinese and English, meaning that getting around the city is easy for most western visitors (although you should always expect hilariously badly translated signs and menus). Similarly, there are a huge number of bars and restaurants that cater to lǎowài expats and tourists - it is relatively easy to do your thing in Shanghai without needing to overcome the language barrier, and for this reason many feel that it is not the ideal city in which to study Mandarin. The truth is that while you can get by with only English in Shanghai, learning even just some basic Mandarin will open up many new opportunities to a foreigner living here, and make adapting to life in China far easier.

Shanghai is undoubtedly China, but certainly not the authentic 'China experience' that you will get from living in smaller cities and towns. However, don't think that this should dilute your experience of China.

Lǎowài living
Even given the rapid westernisation of the city, many visitors often still find it difficult to acclimatise to life in Shanghai. Reading up on cultural differences will certainly help you understand and overcome some of the main ways in which living in China differs from your homeland, but the best way to acclimatise to life here is simply to dive in and experience as much as possible.

It's easy to get trapped inside your own little 'lǎowài bubble' - and compared with the rest of China, Shanghai makes it easy to do so - but you'll get far more out of the city by leaving your apartment, exploring your neighbourhood, trying every weird and wonderful food you see, and trying your best to engage locals in conversation.

This doesn't mean that you need to 'live like a local' in order to enjoy life in Shanghai, but there is a certainly a happy medium to be found. Many foreigners live in Shanghai for years and frequent only bars and restaurants catering specifically to lǎowài (for example, Element Fresh, Wagas, or Blue Frog): while this is perfectly fine for those happy to stay in their comfort zone, many would argue that these people are missing out on a lot of the best things Shanghai has to offer.

Here is a relevant thread from /r/shanghai discussing living an "authentic" lifestyle in Shanghai.

And always remember: TIC.