How can I determine a timezone by the UTC offset?

Short answer: you can’t.

Daylight saving time make it impossible. For example, there is no way to determine, solely from UTC offset, the difference between Arizona and California in the summer, or Arizona and New Mexico in the winter (since Arizona does not observe DST).

There is also the issue of what time different countries observe DST. For example, in the US DST starts earlier and ends later than in Europe.

A close guess is possible (i.e. +/- an hour), but if you are using it to display time to users you will inevitably display the wrong time to some of them.

Update: From the comments, it looks like your primary goal is to display a timestamp in the user’s local timezone. If that is what you want to do, you should send the time as a UTC timestamp, and then just rewrite it on the user’s browser with Javascript. In the case that they don’t have Javascript enabled, they would still see a usable UTC timestamp. Here is a function I came up with in this question, which I used in this Greasemonkey script. You may want to tweak it to suit your needs.

//@param timestamp An ISO-8601 timestamp in the form YYYY-MM-DDTHH:MM:SS±HH:MM
//Note: Some other valid ISO-8601 timestamps are not accepted by this function
function parseISO8601(timestamp)
{
  var regex = new RegExp("^([\\d]{4})-([\\d]{2})-([\\d]{2})T([\\d]{2}):([\\d]{2}):([\\d]{2})([\\+\\-])([\\d]{2}):([\\d]{2})$");
  var matches = regex.exec(timestamp);
  if(matches != null)
  {
    var offset = parseInt(matches[8], 10) * 60 + parseInt(matches[9], 10);
    if(matches[7] == "-")
      offset = -offset;

    return new Date(
      Date.UTC(
        parseInt(matches[1], 10),
        parseInt(matches[2], 10) - 1,
        parseInt(matches[3], 10),
        parseInt(matches[4], 10),
        parseInt(matches[5], 10),
        parseInt(matches[6], 10)
      ) - offset*60*1000
    );
  }
  return null;
}

Here is a function I use on my blog to display a parsed timestamp in the user’s local timezone. Again, you can tweak it to the format you want.

var weekDays = new Array("Sunday", "Monday", "Tuesday", "Wednesday",
        "Thursday", "Friday", "Saturday");
var months = new Array("January", "February", "March", "April", "May", "June",
        "July", "August", "September", "October", "November", "December");

function toLocalTime(date)
{
  var hour = date.getHours();
  var ampm = (hour < 12 ? "am" : "pm");
  hour = (hour + 11)%12 + 1;

  var minutes = date.getMinutes();
  if(minutes < 10)
    minutes = "0" + minutes;

  return weekDays[date.getDay()] + ", "
       + months[date.getMonth()] + " "
       + date.getDate()          + ", "
       + date.getFullYear()      + " at "
       + hour                    + ":"
       + minutes                 + " "
       + ampm;
}