This is a very important day for you and your boat. First the survey....should be done on the hard and not in the water. When your surveyor is done he will go though every system on your boat and if their are any problems will discuss them you. You will get a book that he has put together for your records of everything he has done and the results in writing.
Are you getting a mechanical survey also? This can be helpful if have questions about the engine/s or outdrives, but usually not included in a regular survey.
Any problems use that against the selling price as leverage.
The sea trial is the final chapter is your pursuit of this boat to let you know if this is the boat for you. Let the surveyor drive the boat and you watch and listen. Everything from top speed (using his GPS and not the boat's speedometer) to checking for leaks, noises and general getting up on plane processes that the boat should do with out issues. If there are issues discuss them and again can be used as leverage at closing for the price of the boat. This is a new boat for you so ask questions!
Good luck and let us know how you did. Pictures are good too!