怎么 (zěnme) and 怎么样 (zěnmeyàng) both translate as "how", but they sit in different places. 怎么 goes before a verb and asks how to do something, or why something is happening. 怎么样 usually comes at the end and asks what something is like, or what someone thinks of an idea.
怎么 + verb.
Put 怎么 straight before the verb to ask about the way something is done: how to read a character, how to cook a dish, how you are getting somewhere. In the answer, the method goes in the same place, before the verb: 你们怎么去？ 我们坐飞机去。 There is no 吗 at the end, because 怎么 already makes it a question.
怎么 can also ask why, when you are surprised or a little annoyed. It is often followed by 不, 没有 or 还: 你怎么不说话？ means "Why aren't you saying anything?". It sounds like "how come" in English. Later you will meet 为什么, the plain word for "why".
你怎么了？ is a very common question. It means "What's wrong?" or "What happened to you?" when someone looks ill, sad or upset.
Thing or person + 怎么样？
Put 怎么样 after the thing you are asking about to ask what it is like or how it is going: a new job, a film, the weather, a teacher. You can also say 你觉得……怎么样？ (What do you think of ...?). Answer with an adjective, usually with 很 or 太: 很好, 很好吃, 太贵了. 你怎么样？ on its own means "How are you doing?".
To make a suggestion, say your idea first and then add 怎么样 at the end, like "how about it?" or "is that OK?" in English. To agree, say 好的 or 好.
The most common mistake is to swap the two words. 怎么 cannot end a question about what something is like: say 今天天气怎么样？, not 今天天气怎么？ And 怎么样 cannot mean "why": say 你怎么不喝茶？, not 你怎么样不喝茶？ A simple rule: before a verb, use 怎么; at the end of the sentence, use 怎么样.
Two more mistakes: putting 怎么 after the verb (你去怎么医院 is wrong; say 你怎么去医院), and adding 吗 to a question that already has 怎么 or 怎么样 (你的老师怎么样吗 is wrong).
Practise this grammar point on paper: 20 exercises using only HSK 1 words, with an answer key on a separate page. Free to print and copy for your class.
Every example on this page uses only words up to HSK 1. Paste your own sentences into the level checker to see which words, if any, are above your level.