How can I translate cultural terms when they have no equivalence in the other language?

There is always a way to translate it. Talk with native speaker or try to find out good explanation of the word and add it to the translation.

As said by  Aleksandra Hadrik, a way is always there to have it translated. Understanding the culture of the others is useful and can help in producing a successful translation. Translation is not a speciality, but it all relates to skills and capabilities.

A translator should be creative; to be creative you need to read more about other people's cultures and environment

First of all we should know that there is no equivalent for each and every word between languages, and second we need to focus on the main meaning of a language, and simply a language is a way of communication and delivering ideas, so a good translation doesn’t have to be literal; it is what delivers the comprehensive meaning of the context. last and not least general reading and good grammar structure are milestones in understanding cultures and excelling in lingual translation.

Thuraiya this will be very easy for any TEFL teacher if they know the proper way. I will tell you how. Just Describe the cultural term in detail to your students. Tell them what happens on that occasion. Give examples and show picutre cards. You can also use sign language from time to time. When you feel that they have begun to understand, just tell them that it's named so and so in that particular language, write it on the board and tell them its significance. 

I can give you a small example here....

In our Indian culture we celebrate 'DIWALI'. This is one of the main festivals of India just as EID is for muslim culture and CHRISTMAS is for Christian culture. It's celebrated with the same enthusiasm and zeal as the others and it signifies the victory of goodness over the evil. It's a festival of lights and the whole country is lit with beautiful lights all over and people enjoy it by bursting crackers and distributing sweets while they visit and wish each other for prosperity and success. At this point you can also show some pictures to make yourself clearer to them.

So, Turaiya, I think I have answered your question to your satisfaction. You are welcome to ask if you still have any queries regarding your intelligent and valuable question. Good Luck! 

you either translate the idea or find the proverb in the target language