For example, Galaxy NGC 3689 has the right ascension of 11:28:11 and declination of +25:39:40.0. Using these values, how can we find the distance to the galaxy? If it helps, its radial velocity is 2727 km/s.
You can't use the RA and dec. These tell you the direction that the galaxy is in, relative to the stars. It is possible and normal for two galaxies to have the same (or very similar) RA and dec and be at completely different distance.
You can estimate the distance using the Hubble law $v= H_0 d$, if $v$ is measured in km/s and d is in mega-parsecs the value of H_0 is approximately 70 (measuring this value accurately is a major problem in cosmology)
So $D= 2727/70 \approx 39$ So we estimate the distance to the galaxy to be 39 million parsecs (multiply by 3.26 to convert to millions of lightyears). This can only be an estimate, as the actual value of $H_0$ is not know with certainty, and the galaxy can have particular motion relative to the Hubble flow (for example, Andromeda is actually blue shifted, but it isn't a negative distance from us, as this value would suggest!)