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The Lorentz factor gamma = 1/sqrt(1 - v^2/c^2) governs every relativistic effect. At 0.6c it is 1.25, so a one-second interval on the moving clock stretches to 1.25 s for a stationary observer, and lengths contract to 0.8 of their rest value. Below 0.1c gamma is within 0.5% of one, which is why classical mechanics works so well.
Lorentz factor
gamma = 1 / sqrt(1 - v^2 / c^2)
Time dilation
dt = gamma x d(tau)
About 0.866c. Time then runs at half the rate and lengths halve in the observer's frame.
Routinely - muon lifetimes in cosmic rays, atomic clocks on aircraft, and GPS satellites all require the correction to work.