Missions and Objectives are assigned to you at key points in the game. A mission is usually a primary, long range goal. In order to complete your mission usually consists of completing one or more short term objectives.
You are normally informed by the game when you are assigned a new objective, usually given by Sergeant Kelly. You are not always informed of a change of mission though, especially when you transfer from one level to the next. You will need to manually check your PDA from time to time to see if your mission has changed.
The reality is that Missions and Objectives have been implemented fairly loosely by id. On occasions, without warning, your current mission and object is replaced by a completely new set even though you haven't completed them. You will just have to roll with this limitation.
Below is a table of all the Missions and Objectives found in the game, where they are assigned and where they are completed. I've also supplied detailed text for each mission and objective for easy reference.
The table is listed in the chronological order in which you find the Missions and Objectives in the game.
Security Clearance Updates are usually granted when you pick up a character's PDA that has a specific, non general access Security Level set. When you pick up the PDA you are informed by the game, but this is often overlooked in the heat of the moment. On one ocassion Sergeant Kelly remotely updates your clearance for you.
When your security clearance has been updated you are able to open up new areas that were previously locked away from you in the game. Occasionally however, there seems to be no purpose to the new security clearance.
Below is a table of all the Security Clearance Update that occur in the game, where they occur and how you get the update.
The table is listed in the chronological order in which you obtain the Security Clearance Update.