How to calculate the heliocentric velocity of an object?

The heliocentric velocity $V_mathrm{H}$ of an object is its velocity wrt. the Sun. When you measure an object's velocity, you measure it in the reference frame of Earth, which revolves around the Sun with ~30 km/s (varying a bit from aphelion to perihelion), so convert to $V_mathrm{H}$ you need to know the time of the year of the observation (unless the line of sight toward your object is exactly perpendicular to the ecliptic plane), as well as the angle between the line of sight, and the line of sight toward the Sun. This involves a number of sines and cosines that you can find in e.g. Barbieri (2006).

If you further want to convert from $V_mathrm{H}$ to the reference frame in which the Milky Way's center is at rest, the Local Group is at rest, or the Cosmic Microwave Background is isotropic (the "cosmic" frame), then you use the formula you link to, adding a similar term as described above, but instead using the velocity (i.e. speed and direction) of the Sun wrt. to the given frame.