The sole official language of Malaysia is Malay (Bahasa Malaysia or colloquially, Bahasa Melayu), which is very similar and to a large extent, mutually intelligible with Indonesian. Some parts of Malaysia near the Thai border, most notably Kelantan, have dialects of Malay which are nearly incomprehensible to speakers of standard Malay, though most people in these areas will be able to converse in standard Malay if needed.
English is compulsory in all schools and widely spoken in the larger cities, although in rural areas a little Malay will come in handy. There is also a colloquial form of English spoken among Malaysians in urban areas, not inappropriately known as Manglish, which takes a bit of getting used to if you intend to join in the conversation on local topics. Malaysians will almost always try to speak 'standardized English' when approached by Western travellers. In general, police stations and government offices will have English-speaking staff on duty.
Arabic is taught to those who attend Islamic religious schools, and many clerics as well as other very observant Muslims will have a functional command of Arabic. However, it is not widely spoken, though the Malay language does have a large number of loan words from Arabic. You also might notice some examples of Malay written with Arabic letters. This is called Jawi, and it is still used for religious publications and inscriptions, especially in conservative states like Kelantan, although the Latin alphabet is much more commonly used throughout the country.
The Chinese community in Malaysia speaks a wide variety of Chinese dialects including Cantonese, Mandarin, Teo-chew, Hakka, Hainanese, Hok-chew and Hokkien. Mandarin is taught in most Chinese schools while Cantonese is commonly heard in the mass media, so most Malaysian Chinese would be conversant in both, regardless of their native dialect. The most commonly spoken Indian language is Tamil; others include Malayalam, Punjabi and Telugu.
In the northern states of Peninsular Malaysia bordering Thailand, there are various ethnic Thai communities, known locally as the Orang Siam, who speak various dialects of Thai. Malacca in the south is also home to a Portuguese community which speaks a Portuguese based creole. The remote forest areas of Peninsular Malaysia are also home to various tribal people known as the Orang Asli, who speak various indigenous languages such as Semelai, Temuan and many others. In East Malaysia several indigenous languages are also spoken, especially Iban and Kadazan.