How start a family portraits?

I have a Nikon D60 with two lens that are 200 lens and a 55 lens that i got from my grandparentsfpr & got for my 22 birthday since i do good photograph Sky's and clouds pictures but i wanna start be a professional family portraits for my side job but what do i need to know to make a good professional family portraits like this family portraits in this picture? do i need go to a studio?

You need to know how to operate your camera to achieve the effects you desire in your picture. You need to know what aperture, ISO, and shutter speed are and how they relate to one another.
You need to understand various lighting setups and know which one will be most flattering for the subject(s) you're photographing.
You need to have better equipment than an entry level camera body and cheap consumer glass to go on it. The camera body can work, but you really need good fast glass if you want to be a professional portrait photographer.

In short, you have a long way to go before you're ready to be a professional photographer.

Neither of the lenses you say you have are appropriate for family portraits. The example you show is a poor example of high key as it is underexposed and the texture of the backdrop is visible. To do that type of portrait you need to study posing and studio lighting. Then invest in the proper equipment.

Set your sights higher than that linked shot.
That is NOT a good family portrait.
It is soft overall, the lighting is not good, the "effect" is badly done, the background is a mess and the composition is bad (cutting feet etc).

To be a portrait photographer you need to know all about lighting and how to use it. Both natural and studio lighting. You also need to have "people skills" which can be learnt and you need to know all about posing and composition.

It takes time to learn all that so start now.