Most people don't learn English because they have a love of languages. Most adults are learning English for a purpose, whether it be to pass an exam, for business, their career or to go on holiday. So when deciding what vocabulary to teach them, you need to choose vocabulary which is useful or necessary for them.
The problem with adult classes in doing this is that they all have their own interests (e.g. football, technology, fashion etc...) and reasons for learning English (career, job hunting, business, travel etc...). If students aren't interested in the vocabulary they are learning, they'll just get bored and unmotivated. For a teacher choosing the right vocabulary to teach in class can be difficult.
How to choose the right vocabulary
There are certain topics which are useful or necessary for everybody to learn (e.g. food, expressing opinion, complaining etc...). But to find out what other vocabulary topics your students want to learn, you need to ask them.
I find it useful to ask the students to create a list of 10 vocabulary topics they want to learn in class (give it them to do at home, it gives them time to think about it). Then in the following class, I compare the lists and in front of the class write the most popular topics on a black/white board. By doing this, you'll now know what vocabulary will keep your students happy.
If any students need or want to learn a vocabulary topic which you don't think other students will want to (e.g. writing a CV/resume), set this as individual homework or point them in the direction of resources they can use. I find online/web resources (like the exercises here on blair english) are very useful for doing this. With these, students can do the exercises by themselves and you don't have to mark their answers.
Once you've decided the vocabulary topics you're going to teach in class, the next question is 'how are you going to teach them?'.
Using context to learn vocabulary
The biggest problem I find when students learn new English words and phrases is that they quickly forget them. It goes in one hear and out the other. But how can you stop this from happening?
For example, with the phrasal verb 'to come up with'. What do you think would be the best way for students to learn and understand its meaning and use?
Would it be for you to tell your students its meaning?:
'The first time you think of something like an idea or plan.'
Or would they understand it better if they saw it in a sentence and had to work out the meaning themselves from the context?:
'I came up with the idea of selling mobile phones on the internet when I was in the bath. I always have my best ideas there.'
In my experience, using context (the rest of the sentence, the situation and the topic which a word or phrase is used in) to teach English vocabulary is by far the most successful method to use with your students. It's the process how we all normally learn the meaning of new words and phrases in our own language.
The actual process of students having to work out themselves what the meaning of a word or phrase is from the context actually aids in getting the students to not only understand it, but also to remember better it. I also find that they get a satisfaction from learning the meaning of a word or phrase by themselves rather than being told what the meaning is.
This is the approach you should be using in your classes to teach English vocabulary. Use material and give examples where the meaning of words or phrases can be worked out from the context by the students themselves.
Where to find material
Although you can use any type of text (like a news article from a newspaper or website) to do this, it is easier to teach English vocabulary using texts which have been especially written for the purpose of teaching specific words. Every English student text book will contain reading exercises which teach vocabulary meaning through context. In addition, all the student vocabulary exercises on this website have been designed to explain the meaning of vocabulary through context as well.
This sounds perfect, but there is a problem, context doesn't always help in explaining meaning. I myself used an English word for over 5 years with the incorrect meaning, because I incorrectly guessed what its meaning was from the context I originally heard it in. So if it is easy for me to do, imagine how easy it for your students who are learning English as a second language to incorrectly guess the meaning of a word through the context.
If you find that your students are stuck or have guessed the meaning of a word or phrase incorrectly, try not to tell them the meaning or translate it into their own language. Try giving them another example of when the word or phrase is used and get the students to compare the two examples. This normally helps them in working out the meaning.
I have also found that some students panic when you try to directly help them in class (not wanting to look stupid in front of other student is the main reason). In this situation, I find it more useful to write the second example on the white/black board and leave them to work out the meaning themselves. Return a little later to see if they have worked out the meaning.
Practising new words
I know that this is obvious, but when your students have learnt the new words or phrases you need to get them to use them. Not just reusing the words or phrases in the answers in a set exercise, but getting the students to use them in their own words. Make sure that they try to use them in a conversation or role play with other students, or write their own sentences or essay with them.
Also, make sure they pronounce the word or phrase correctly.
Repetition is good
Once they have understood what the meaning of a word or phrase is, getting them to use it repeatedly is of great benefit. The more they use the words and phrases in their own words, the more likely they will continue to use them in the future.
One of the worst things we can do as English teachers (of which I am also guilty) is to teach our students new vocabulary in one class and never get the students to have to use it in future classes. If they don't use the new words or phrases frequently soon after they have learnt them, they are less likely to use them in the future.
To avoid this, I would recommend that you start every class with a 5-10 minute conversation. Choose a topic for the conversation which the words or phrases they have learnt in the previous class(es) can be reused in (even prompting them to use them if necessary).
Making sure that both the vocabulary taught in class is relevant to the majority of the students and that you use context to get students to learn it, makes in my opinion happier and more productive adult English classes.
But getting students to guess vocabulary meaning through context isn't just about making the classes (and your life) easier. Using context to learn meaning is an essential skill that your students need to know for the future. The students we have today won't be going to English class forever. It is part of our responsibility as English teachers (sorry to sound pompous) to make sure that they can continue improving their English by themselves and without the need for us.