What are the steps between the spacecraft launch and the spacecraft being in position to dock to the ISS?
This varies from vehicle to vehicle. Some vehicles dock to the ISS, others berth with the ISS. Some vehicles do it very quickly, others take days. Amongst those that dock, there are a number of docking ports on the ISS. The timing of the operation, whether the vehicle docks or berths, and location and orientation of the docking port or berthing box make for widely varying sets of steps. I'll look at things from the perspective of how the Japanese HTV berths with the ISS. Orbital's Cygnus and SpaceX's Dragon follow a very similar pattern.
The first phase of flight is launch. Typically the vehicle that will eventually dock or berth with the ISS is a passive payload during this initial phase; it's the launch vehicle that is in charge. This phase ends with orbit insertion.
The insertion orbit may be rather low, so low that the vehicle would reenter in short order without boosting to a higher orbit. This higher orbit is a phasing orbit, one whose altitude is lower than that of the ISS. This lower altitude means the orbital period is faster than than of the ISS. How much time is spent in this phasing orbit (or phasing orbits; some vehicles use more than one) depends on how far the ISS (the target vehicle) is ahead of the vehicle in question (the chaser vehicle). Some vehicles (e.g., the European ATV) might spend multiple weeks in their phasing orbit(s).
When the timing is right, the chaser will raise its altitude so that it is ideally a pre-planned distance behind the ISS. This is not a Hohmann transfer. It is instead a sequence of burns that target a specific point in space at a specific point in time. One approach to doing this is to use Lambert targeting, or some modification thereof. The start of this sequence of burns marks the start of the far-field rendezvous phase of flight.
When the vehicle reaches the aim point (typically hundreds of kilometers behind the ISS), it performs another burn that makes its perigee a bit smaller than that of the ISS. With time, this moves the vehicle toward the ISS. At some point, the vehicle comes within communications range of the ISS. This marks the transition from far-field to near-field rendezvous.
During far-field ops, the HTV (and Cygnus and Dragon) uses GPS to correct its navigated state. The ISS also uses GPS, but the distance between the two vehicles means that the ISS and the chaser may be using different sets of GPS satellites to estimate their state. Once the HTV (or Cygnus or Dragon) comes within in comm range, it switches to using relative GPS. This significantly increases the accuracy of the estimate of the relative state between the two vehicles.
Once the chaser comes within a prescribed distance of the ISS, it switches from near-field rendezvous to approach. In the case of HTV (and Cygnus and Dragon), the vehicle switches at this time from using relative GPS to visual navigation. GPS on the Earth doesn't work as well in cities as it does out in the country because of signals bouncing off of tall buildings (the multipath problem). Relative GPS doesn't work very well in the close vicinity of the ISS for the same reason.
During the approach phase, the chaser must follow a prescribed corridor that eventually bring it to the docking port or berthing box. The approach phase has a number of hold points where the chaser is to come to rest with respect to the ISS. Deviations outside of the corridor or failure to stop at a hold point are signs that the vehicle needs to transition to yet another mode, abort or retreat. There are multiple decision points along the way where the chaser (or the human controllers on the ground) will decide that the best thing to do is either abort or retreat.
The very last phase is of course the actual docking or berthing.