Other than surrounding yourselves with lots of english related items, one of the most essentials is a good dictionary.
Here is a good online dictionary which I would recommend:
http://dict.sztaki.hu/hungarian-english

Sztaki

How to choose a good dictionary if you need it for good oral english or speaking skills?

1. Phonetic transcription
Get a good dictionary that gives phonetic transcription for every word.

2. Examples sentences
Example sentences are English sentences which contain the word.
Some dictionaries give them after the definition of a word.

As a first dictionary, the recommended one will be:
Collins COBUILD Advanced Learner's English Dictionary

For small but informative dictionary:
You can take everywhere you go, the recommended:
Oxford Learner's Pocket Dictionary.