Both “和” and “及” are conjunctions for connecting two words or phrases.
- 和 [hé] : To connect nouns, verbs or phrases, not necessarily expressing a relationship and often informally. E.g. 汽车和现金 (car and cash),
蓝宝石和翡翠 (sapphire and jade).
- 及 [jí] : Mostly used in writing to connect nouns, with greater emphasis on the items preceding it. E.g. “囧”字的读音、意思及其常用表现手法
Example of combined usage adapted from Google's policy:
Note the order and how “和” is used to join the larger phrases together.
Difference between 与，和 and 跟?
There are a lot characters meaning "and": 和/及/与/而/又/并/同/亦/且/兼/跟"
面包 和 黄油 bread and butter
一个女人﹑ 两个男人 及 三个孩子 one woman, two men and three children
《儿子 与 情人》 Sons and Lovers
缓慢 而 仔细地 slowly and carefully
能读 又 能写 able to read and write
他为她感到难过， 并 试图使她振作起来。 He was sorry for her and tried to cheer her up.
你 同 他一起去。You and he go together.
他生 亦 穷来死 亦 穷。He was born poor and died poor.
一个优雅 且 和蔼的女人 a graceful and gentle woman
他担任教练 兼 队长。He doubled as coach and captain of the team.
你 跟 他一块儿来。You and he come togther.
It is very hard to give specific rules on how to use them. You need to read a lot Chinese text to build up your language sense on those characters. But one rule seems holding the water all the time: if there are mutliple level things in the same sentence to be joined by "and", then you will need to use different characters.