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Some airlines have group desks or departments which will deal with individuals. You can sometimes find the group desk contact info on the airline's website, otherwise just call their reservation center and ask for the group department.
Other airlines only sell through travel agencies.
In general group rates are not really that much of a bargain, you can often find better fares buying tickets individually. But group fares do have some advantage in terms of blocking space before paying, less restrictions and assurances that your group will likely be seated near each other (usually the center section).
There are really no tricks, they will simply look at the routes you are interested in, your group size, time of year and will kick out a pre-determined price. There is not much negotiating to be done or insider angles, unless you are moving hundreds of passengers.