The actual actual space flight mission could be described and performed in many different ways, but the original NASA surveyor class mission has a strong sense of simplicity which should not be underestimated.
So the steps to the moon:
(and all the preparation that went before!)
2) Staging, oayload shroud jettison, Booster burnout 6-16 minutes
3) Vehicle separation 1-90 minutes
Kick it off with small springs and some thermal release mechanisms (heated wire cutters)
4) Trans-lunar injection makeup. 1-15 minutes
This may be almost nothing like in surveyor, or it may be a very significant burn with attendant attitude and position determination. It is possible that the launch vehicle may not even deposit the lunar stages into an orbit. mass and propellant trades need to be done with the chosen system. In other words the vehicle is the upper stage !
5) Coast phase. up to 5 days
The vehicle will find a stable attitude with simple sensors holding this attitude fix and probably some rotation. Small solar panels can produce power, Communications will be sent and received with the ground. Either ground based tracking or GPS/Navstar onboard receivers will refine the position and velocity vectors of the vehicle.
6) Midcourse correction(s) 1-5 minutes
As necessary, engine firings can be used to refine the lunar trajectory. Surveyor planned on one, more may be required. After firing the engines,thevehicle will return to its coast attitude.
7) Landing initation 1-10 minutes
Depending on the tracking accuracy and range of the (Li/Ra)dar, the landing sequence may be initiated by ground command or lunar proximity.
8) Breaking 9 minutes
There is a whole bunch of speed that needs to be bled off with plenty of rocket impulse. This, in many ways is like flying the launch vehicle profile in reverse from escape velocity right down to vehicle pitchover. Similar attitude and thrust profiles are used.
9) Landing. 1-2 minutes
The vehicle is now low and slow over the lunar surface. It is now important to have controllable thrust levels on par with the gravitational force of the moon. This probably means that the main engines will have to be throttleable, selectively shut down, or both. Another option is to land on very small engines, even possibly redundant attitude jets. This last option actually looks very good given the very small remaining fraction of propellant left (mass) and the low gravity(weight/mass). Also during this phase any residual lateral motion has to be removed and the attitude and sink rates broght within landing gear limits(whatever that is designed for).
10+) Hopping 3 minutes
With remaining propellant, the vehicle can ascend and repeat the landing manuver in a different location.
The surveyor spacecraft used three vernier engines for landing and one large solid for much of the breaking. It also had six small cold-gas attitude jets for the coast phase.