Every syllable has a citation tone - and running speech rewrites some of them. Four rules cover almost all of it.
Third-tone sandhi
Two third tones in a row: the first becomes second. 你好 is written nǐhǎo, said níhǎo. 很好, 我想 - same rule. In longer chains (我姐姐也很好） the rhythm groups decide which syllables shift, but the pairwise rule gets you 90% there.
不 and 一
不 is fourth tone everywhere except before another fourth tone, where it becomes second: 不是 bù→bú shì, 不要 bú yào. 一 shifts before fourth tone to yí (一个 yí ge, 一定 yídìng) and before first/second/ third tones to yì (一天 yìtiān, 一年 yìnián, 一点 yìdiǎn); it stays yī only as a bare number or ordinal (第一, 十一). Note: dictionaries and the dictionary pages print citation forms - the surface reading is what you say.
Neutral tone
Unstressed syllables drop to a short flat pitch that rides the previous tone: 妈妈 māma, 我们 wǒmen, the particles 的了吗呢吧. It is not "tone 5" - it is no tone. Some pairs change meaning by it: 东西 dōngxi (thing) vs dōngxī (east-west), 大意 dàyì (gist) vs dàyi (careless).
Erhua (儿化)
Beijing Mandarin folds a -r into many syllables: 一点儿 yìdiǎnr, 哪儿 nǎr, 玩儿 wánr. It is regional - Taiwan speech largely lacks it - but northern audio will run it into everything. Hear it, don't force it.
Common questions
What is tone sandhi in Mandarin?
Tone change in context: two third tones make the first a second tone (nǐhǎo → níhǎo), 不 becomes bú before fourth tone, and 一 shifts by the following tone.
Is 不 always fourth tone?
No - bú before a fourth tone (不是 búshì, 不要 búyào), bù elsewhere. Learners who miss this are still understood, but it is the single most audible non-native marker.
What is the neutral tone in Chinese?
An unstressed syllable with no contour of its own - 妈妈 māma, particles like 吗/了/的. Some minimal pairs differ only by it: dōngxi (thing) vs dōngxī (east-west).