The Beijing dialect is probably the most well-known dialect among Chinese speakers. With its symbolic accent and special greetings, 北京话 (Běi jīng huà) is the very pride of people who grew up in this city. And when you speak Chinese with a Beijing accent, it will natually bring you closer to the locals.
1 Use 您 (formal) instead of 你 (informal)
In stardard Mandarin, or putonghua (普通话), it is taught that 您 the honorific form of 你. While the former is used in formal situations and with elders, the latter is used with peers in daily speech. In the Beijing dialect, however, this is not strictly the case. People from Beijing always address strangers with 您 instead of 你, regardless of your age or the other person's age. This seemingly formal pronoun is also used among relatives and neighbors who already know each other well (a situation where you should definitely use 你 in standard Mandarin). When 您 is used by an elder to a youngster or a friend of similar age, it adds a sense of irony or satire to the sentence.
Thank you for this feast you bought me (After a "feast" of only one unpalatable dish in a cheap restaurant).
2 Use 甭 (béng) instead of 别 (bié)
别 (bié) is commonly used in negative imperative in standard Mandarin. In the Beijing dialect, this character is often replaced by 甭 (béng). However, the two are not semantically identical in some occasions. While 甭 sometimes resembles 不用（bùyòng), or "don't have to" in most situations, 别 is more of a petition asking someone not to do something. The trivial semantic differences require a lot of exposure to the dialect for someone to fully understand.
It's not possible. Don't even think about it.
3 Use 倍儿(bèr) instead of 很 (hěn)
很 (hěn) or 特别 (tè bié) are the Mandarin equivalents of the English adverb "very". In the Beijing dialect, however, 倍儿(bèr) or 特 (tè) are often used in their places. While 倍儿 is more classic and is used more commonly by older people, 特 is more frequently used by the younger generations. 特 has also gradually found its way into standard Chinese and is used by youngsters outside of Beijing as well.
It feels so good to have a beer outside at night these days.
4 Master the Neutral Tone (轻声)
The neutral tone is sometimes known as the "fifth tone" in Mandarin Chinese. It is a distinctive linguitic phenomenon in Mandarin in mainland China (the Mandarin spoeken in Taiwan does not have the neutral tone). If you are familiar with this tone, you probably already know some characters commonly pronounced in the neutral tone, such as 着 (zhe), 了 (le), 的 (de), 吗 (ma), and 吧(ba). Some two-character words such as 妈妈, 爸爸, 聪明 also require the neutral tone for the second character. In the Beijing dialect, however, more words are pronounced with the neutral tone than in putonghua: 清楚 (qīng chu, "clear"), 木匠 (mù jiang, "carpenter") do not contain the neutral tone in standard Mandarin but they do in the Beijing dialect. Unfortunately, there are very few consistent rules regarding the neutral tone. The only way to master it is to do so through exposure to the dialect.
5 Know When to Erhua (儿化)
儿化音 (érhuàyīn), or the rhoticization of syllable finals, is a common phenomenon in various northern dialects of Mandarin Chinese. However, the Beijing dialect takes it to the extreme, making it a symbolic feature of the locals' speech. Normally, the 儿 is added to the end of a word: 好玩儿 (hǎowáer, "fun"), 小孩儿（xiǎoháir, "kid"). But there are also many exceptions such as 板儿砖 (bǎnrzhuān, "brick"). Similar to the neutral tone, it is very difficult to master the 儿化音 phenomenon and the only way to acheive it is consistently listening to native speakers and memorizing each individual word with "er" attached to it.