There's a few things you can do. Cutscenes can be one solution, but they take quite a bit of effort to do and interrupt the player in whatever they were doing. Messages are another thing, but the player may not be paying attention to those if there's no voice acting. The best thing you can probably do is design your mission in such a way that you get little rest points that the player can catch their breath and be more attentive for what you (the FREDder) would like to tell them.
So don't do things like pile up lots of wings to keep coming at the player, or do things that are strictly based on mission time. Sure it may be more "realistic" but it is not very "gameplay friendly".
The best thing I tend to do is break up my mission into small stages. When one stage ends, I give around 30-60 seconds of quiet time, send some messages (and have a great good spot to add checkpoints), then proceed to the next action sequence.
Play some of your favorite missions and see if you can spot how they get your attention.