You should not go into construction mode. Just get a Kerbal close enough to the storage to drag and drop items to/from the Kerbals inventory.

Items that get deployed

Grand Slam seismic device

Mystery Goo device

Ion Collection - airless only

Weather Station - atmosphere only

Control Station

Power units - either deployed solar panels or nukes <should be deployed by engineer>

Transmitter




Items underlined in red need to be placed in Kerbal's inventory to get deploy option.

You have to place the item into the Kerbals personal inventory.

Once you have it equipped on the character you will have a deploy icon on the items picture in the lower corner. You must click on the deploy icon to get the deploy options for placement.


An Engineer should deploy the power supply parts for maximum output.

A Scientist should deploy the experiments for maximum output.

Note - Experience level on the Scientist or Engineer will also effect the amount produced when deployed. Other parts it won't matter and even a Pilot can place them.

Interact with items to make sure they are powered and connected.
Science will collect over time for most things, the seismic device only takes a single reading when you crash something near it.



Now you wait.... it will take some time to build up and transmit so it is best to do other things while it works.
Every so often you will get a report some science has transmitted until it is complete. It is at regular intervals but the time will change depending on how fast the science collects based off the level of the scientist who placed it.

NOTE:
Currently it seems the solar panels do not always show output on their own interface. They do show output on the control box so they are putting out, just a false UI issue.

It has been reported that there may be some issues using the parts if you have mods.

A user has reported needing to place the control unit last for it to work. I tested the game repeatedly and this was not needed in an unmodded game.

If someone can verify the issue and post back that would be appreciated.

I did see a KOS window on the control box for the experiments in the persons screeshot but do not know if that mod is the problem or not.