The customer is always right (unless you are blatantly disrespected or dealing with an unruly intoxicated person). Always bring a new cocktail napkin with each drink. Wipe down tables as often as you need to, but do it unobtrusively when you bring new drinks or take a finished one away. This means picking up all empty glassware and plates, as well as used napkins and trash, and emptying ashtrays if you're in a state that still allows smoking in bars. Keep it tidy! Make sure your customers' area is neat and clean.
If you are paying attention you can keep a running list of everything you need to attend to in your mind.
Keeping focused and organized will help you get to your tables faster and get their orders in quickly and correctly.