Try your best to focus on your breath and only your breath. Have your eyes contemplate your nose, your nose contemplate your upper lip, and the upper lip contemplate the heart. If you are able to do this and truly focus on your breath without false thoughts, you should be able to enter a state before the first jhana in which you'll experience a lot of joy, but do not be attached to the state. You'll know when you run into the state.
As a side note, false thoughts don't disappear until you have truly purified the mind. Until then, do your best to concentrate solely on breath or buddha-name recitation and try not to let your mind wander. It is extremely difficult, but if you try hard to watch your mind and bring it back to the breath then you can enter dhyana. Also, avoid meat and the five pungent plants as they can disturb your mind and cause restlessness.