
In cases where you do need to use them, try to stick to a plain verb as much as possible, rather than adding too many adverbs. Here are a couple of examples:
1) He said softly
This could be rendered as 'He murmured' or 'He whispered'.
2) He walked quickly
Here you could go for He dashed, He hurried, He hastened, He strode etc.
See how the single verbs pack more punch and add some flavour to the narration? The choice of verb is important. Think of the different sense of the scene you get by choosing 'he dashed' over 'he strode'. The first has a feeling of urgency; the second imbues him with purpose.