This is a straightforward extension of the 2D translation transformation:
(1 0 0 0)
(x' y' z' 1) = (x y z 1) * (0 1 0 0)
(0 0 1 0)
(Tx Ty Tz 1)
which gives: x' = x + Tx
y' = y + Ty
z' = z + Tz
Note: to do an inverse Translation in 3D, replace Tx with -Tx, Ty with -Ty, and Tz with -Tz then T (T-1) = 1 (identity matrix)