In the West, Chinese has an undeserved reputation for its difficulty. It is very different from Western languages, but basic grammar is pretty simple. Verbs are static regardless of whether they are referring to the past, present or future. Genders of nouns do not exist, and there is no separate form of nouns for plurals. The main difficulties are the existence of several consonants not present in Western languages and using tones.
Mandarin is a tonal language that uses a pitch in sounds to inflict different meanings. Ma could mean mother, horse, numb, blame, depending on tones. Homophones are also common. The same sound at the same pitch usually has dozens of meanings. Zhong1 (Zhong at the lst tone) can mean China, loyalty, clock, chime, finish, a bowl, etc. Homophones are not a problem in everyday conversation, but it is very common for Chinese to ask how to write someone's name by telling the meaning of all characters one by one. "My name is Wang Fei. Wang is the Wang with three strokes, Fei is the fei in shifei(gossip), with a grass on top."
There are, in theory, more than 50,000 Chinese characters. However, 85 percent of these are obsolete or rarely used. To bridge the gap between recognizing and reading out loud, pinyin was developed, which uses Latin script as an aid to teaching Chinese. Pronouncing pinyin is not intuitive for English speakers, as certain letters and consonant clusters are not pronounced as a westerner would expect. Nonetheless, learning it at even a basic level has enormous practical value.
Standard Mandarin is the administrative language, but people native to urban Beijing have a unique dialect which belongs to the Mandarin subdivision of spoken Chinese. The dialect contains nasal "er" sounds at the end of many words. Luckily, modern Mandarin is based on this dialect. Rural areas of Beijing Municipality have their own dialects akin to those of Hebei province, which surrounds Beijing Municipality.
There a variety of schools and ways to learn. You should consider factors of: price, your current knowledge of the language, time you have available, and how fast you want to learn. There are full-time and part-time courses, as well as residential courses (where they offer accommodation).
Many programs people can sign up for that will arrange a trip to Beijing, set-up accommodations, and enrol them in classes. These are usually quite costly, but may be immersion learning and be quite effective. The International Students Center is an example of this. More programs can be found through Go Abroad.
More common are the language schools in which people already residing in Beijing can enroll. Most offer sample lessons or let you sit-in for free before signing up. Shop around before choosing.
More Schools can be found here.
Private lessons are another option. More expensive than language courses, these can be very effective. Expect to pay between 45-80 RMB per hour depending on the tutor's qualifications and experience.
You can search for opportunities in a local newspapers, on message boards at pubs, copy centers, supermarkets, universities, and cafes, or on online boards such as EasyExpat's Job Listings for tutors and classes. You can also find friends on the forum to work on language exchange.