This example allows all users to retrieve any object in MyBucket except those in the MySecretFolder. It also grants put and delete permission to the root user of the AWS account 1234-5678-9012:

aws s3api put-bucket-policy --bucket MyBucket --policy file://policy.json

policy.json:
{
   "Statement": [
      {
         "Effect": "Allow",
         "Principal": "*",
         "Action": "s3:GetObject",
         "Resource": "arn:aws:s3:::MyBucket/*"
      },
      {
         "Effect": "Deny",
         "Principal": "*",
         "Action": "s3:GetObject",
         "Resource": "arn:aws:s3:::MyBucket/MySecretFolder/*"
      },
      {
         "Effect": "Allow",
         "Principal": {
            "AWS": "arn:aws:iam::123456789012:root"
         },
         "Action": [
            "s3:DeleteObject",
            "s3:PutObject"
         ],
         "Resource": "arn:aws:s3:::MyBucket/*"
      }
   ]
}