Universal time is a time scale based on the rotation of the Earth. Because the rotation of the Earth is somewhat irregular, time can not be kept this way with an accuracy better than 1 : 108. Moreover, the Earth slows down in its rotation, mainly because of tidal acceleration: the length of the day increases by about 1.7 ms/century.
For this reason, ephemeris time was introduced, which is a time scale based on the motion of the bodies of the solar system. This time scale is more stable than universal time, and comes close to the accuracy and stability of atomic time measured with atomic clocks (better than 1 : 1012).
So universal time slowly lags behind ephemeris time, and the difference accumulates: this is Delta-T. It increases irregularly, and must be determined from observations; this is maintained by the International Earth Rotation Service (IERS): http://www.iers.org/. Values for Delta-T based on historical and recent observations are available from about 700 BC to the present day ,, but estimates from before systematic observations were made by telescope (17th century) are not very accurate.
Delta-T was 0 in the late 19th century when accurate ephemerides were matched with the clock time, which was based on the rotation of the Earth. It already had accumulated to +32.18 s in 1958 when atomic time was introduced, and to +63.83 s in 2000. See http://www.iers.org/iers/earth/rotation/ut1lod/table1.html for recent values of UT1-TAI, which can easily be converted to Delta-T as indicated (TT is ephemeris time).
http://user.online.be/felixverbelen/dt.htm gives a historical account and more tables with values.
 F.R. Stephenson, L.V. Morrison (1995): "Long-term fluctuations in the Earth's rotation: 700 BC to AD 1990". Phil. Trans. Royal Soc. London Ser.A, pp.165..202 .
 F.R. Stephenson (1997): "Historical Eclipses and Earth's Rotation". Cambridge Univ.Press. ISBN ?