Allowing an IAM user access (Uploading and Deleting) to one of our specific buckets.

Hi Huma, I hope you are doing great. It is not clear for me if the user you are trying to configure will need programmatic access (using the terminal commands) or it needs access through the AWS Management Console.

If your user needs programmatic access, The policy attached to your group should be like the following.

{
  "Version": "2012-10-17",
  "Statement": [
    {
      "Effect": "Allow",
      "Action": ["s3:ListBucket"],
      "Resource": ["arn:aws:s3:::NAME-OF-YOUR-BUCKET"]
    },
    {
      "Effect": "Allow",
      "Action": [
        "s3:PutObject",
        "s3:GetObject",
        "s3:DeleteObject"
      ],
      "Resource": ["arn:aws:s3:::NAME-OF-YOUR-BUCKET/*"]
    }
  ]
}  

If your user needs access through the AWS Management Console, the policy attached to your group should be like the following.

{
  "Version": "2012-10-17",
  "Statement": [
    {
      "Effect": "Allow",
      "Action": [
        "s3:GetBucketLocation",
        "s3:ListAllMyBuckets"
      ],
      "Resource": "*"
    },
    {
      "Effect": "Allow",
      "Action": ["s3:ListBucket"],
      "Resource": ["arn:aws:s3:::NAME-OF-YOUR-BUCKET"]
    },
    {
      "Effect": "Allow",
      "Action": [
        "s3:PutObject",
        "s3:GetObject",
        "s3:DeleteObject"
      ],
      "Resource": ["arn:aws:s3:::NAME-OF-YOUR-BUCKET/*"]
    }
  ]
}

I hope the above helps for your user case.

Have a great week ahead!