For tp's you usually get a phone call about a week before the event asking if your available and legal to fly the type. Sometimes you get asked to provide the other crew others its assigned.
Then if your not on file you email in your papers and sign a contract.
A couple of days before you get through the cunning plan and travel tickets.
At some point you will meet someone and pick up an expenses float and fuel card.
You head off and if your lucky the plane will be waiting for you all signed off and ready to go. If its just out of storage there can be various ball aches until its legal to be flown. Then depending on where you have picked it up from or where you going to the flight can be a complete nightmare of red tape or it could just be a case of light em up fly land and hand the paper work in at the other end.
The specialist ferry boys are masters at the red tape and legalities of getting airframes in and out of various authorites.
I have done 2 one was a doddle and one was a ball ache. Both were good fun but you have to be alot more savy about legalities (and not the stuff the teach you in your ATPLs than you average line pilot).
How did i get them? Word of mouth, someone else couldn't do it and gave them my number.