How can non-English speaking parents help their kids learn and read in English?

to speak between each other in English  

...to choose for them good programes in English

Practice, Practice, Practice.

Speak good English phrases and learn them well.  Keeping own personal style so that it sounds natural.

Read alot of English words.

Write alot of 'English words.

yes i think the role of the parents is very important, whether they speak English or not.

the main thing they can do, is to give their children the needed encouragement and the moral support, than they can provide them with some simple materials like pictures of things with their names, and try to memorize them along with the children. this will make it more fun to the children and make them more willing to learn. 

Teach their children English terms as much as possible by linkage between the word and related thing for this word

And try to speak with them in English as much as possible to motivate them to be used in all aspects of their lives

And made ​​them watch English language learning programs allocated to their "ages"

And watch as much of cartoon films and programs in English

They should introduce certain programmes which are available where by there is a parent guide included with translation in a way the parent benefits and also the child doesn't feel that his parents lack that English knowledge and the programmes are usually  available in levels from basics  the programmes include CDs books and activity books 

Tell their childern that after coming back from school to explane what was given in school so they learn too.   

Grammer is the key of any language. Let their kids learner Grammer, vocabulary is the by-product, gained by the persistent study.

It's only learning, no short cuts. Please refer to the Hadith of our Prophet Mohammad (Peace Be upon Him), " Learn from cradle to grave."

impose the kids to ENGLISH STUFF

There is plenty of ways suchs as : songs / speaking with native speakers  / cartoon films/  reading stories . 

 I think that if they are willing to make their child memorize well the wrods like for example; the stuff  of the kitchen, they can stick to anything inside the kitchen a small paper with it name on it and whenever he need anything, they will spell the word and give it to him if he spell it after them correctly.They can invent or bring logical games that is based on teaching him new words in English. they can bring him cartoon movies and children songs to improve his ability in listening English and learn new languages .

Encouraging them to read more. watch films and listen to English songs