So far as our observations of other young stars seem to be telling us, it began with a collapsing cloud which contracted into a flattened disk. Out of this disk, progressively larger dust grains grew until they got to be golf-ball sized. They then stuck together via low-speed collisions into kilometer-sized bodies. As soon as one of these continued to grow big enough so that its 'cross section' was determined by its gravitational capture radius, its further growth took off and you ended up in a few 100,000 years with a planet-sized mass.
So far, observationally, we have detected these orbiting disks around hundreds of young stars. We have yet to see planets form, but we know that there are other solar systems 'out there', so it's just a matter of time and technology before we will be able to study the whole process in detail.