I'm also a non-native English speaker. You can do couple of things to improve your spoken English, by reading a good website (especially those listed in this site like Natgeo). Just try to read one article everyday and that's what I have been doing. Buy the entire
MGMAT set. Go through Ron's videos, its totally free. These videos are long and lengthy, if you have time, its worth the advice and tips that Ron gives.
Its been one month since I have started my GMAT prep. So far I have been following the above to improve my verbal. Start with
MGMAT foundations for verbal. I strongly recommend you to start from basics if you are not confident. I recommend you to focus on SC, CR and then RC. That's the way I'm training myself. I took about 3 weeks for SC alone. Try to make some cheat sheets for Idioms, grammar rules, so that it might help you to squeeze some time for SC.
Good luck and keep up your faith.