If you are having serious problems or your garden is particularly dense, consider buying a sweep or net to skim around your plants. You might be surprised by the harvest. Of course, not all the bugs you'll find are bad guys. You need to be able to tell them apart. While you were researching about bugs, you've probably come across several recommended solutions.
Different pests mean different solution.
There is no one universal answer, organic or otherwise. One solution might be a change in the overall culture. Lots of problems happen because of high humidity from watering. Maybe you can change to drip irrigation, a method that will change the humidity at plant level. Or, change your watering schedule to early in the day so foliage will be dry before dark.