GMT relates with local standard time as illustrated below :

Basis for Greenwich Mean Time is Greenwich, England (position not shown precisely on map, unfortunately). 0° longitude is the Greenwich Meridian, and poisitive west longtiudes (and latitudes) are labeled (base map obtained from Xerox Parc Map Viewer). Average subsolar point (place on Earth our sun is directly above) is indicated for hourly GMT times. Average is an important word regarding this. The subsolar point varies between -23.44° & +23.44° latitude during a year, and moves approximately 3.7° east/west from its average position during a year, as illustrated for July 25 (position does not change much for the same time each year). Thus, basis for Greenwich Mean Time is mean solar transit time across the Greenwich Meridian (please notice correction) :

UTC (Coordinated Universal Time) is obtained from coordinated measurements at many worldwide observatories and contains small corrections wth respect to GMT. Thus, it is the official time standard, though nearly same as GMT.

As the first diagram indicates, local standard time can be easily calulated if GMT (assumed = UTC for illustration) and base time zone longitude is known. E.g., basis for Eastern Standard Time (EST) is the 75° W meridian, thus :

EST = GMT - 5 hours

If GMT is < 0500, then (obviously) add 24 hours for calculation. I.e., if GMT = 0218,

EST = (2400 + 0218) - 0500 = 2118 = 9:18 PM

Coverting to daylight savings time is as simple as adding an hour (10:18 PM EDT for this example).