If you've understood events and SEXPs you really shouldn't be having that much of a problem with objectives. Like arrival cues for ships and wings, objectives are just a slightly different kind of event.
To make an objective you simply go to the objectives editor. You choose the kind of goal you want (primary, secondary or bonus) and then you make an event that comes true when the goal is achieved.
For instance if you wanted to have an event come true when a ship survives you would do something like this
when
-or
--is-event-true-delay
---all enemies dead
---0
--has-departed-delay
---Ship
---0
The above event makes the objective come true when an event in the events editor called "all enemies dead" becomes true or when the ship has jumped out.
If the ship is destroyed by the enemy, neither of those things can happen and the objective will immediately fail.
Debriefs are handled is basically the same way. Each stage will only be played if the trigger SEXP next to it is true.
The best way to get a handle on this is to actually do the walkthrough that should have come with FRED2. Simply reading it isn't enough for most people. Actually do it. If you're serious about making your own missions the hour or 2 you'll spend on the walkthrough will pay for itself compared with the hours of head scratching you'll do otherwise.
If for some reason you don't have the walkthrough follow the link in my sig and download a copy from my FAQ.
Here's a link to the online version so you can check if you actually have it.