I have one last thing to add on how to make things easier for you. After seeing the screen shot, it looks to me like you are not selecting your units when you enter the dungeon. Here is a little guide on how to do that.
Whenever you select a dungeon to enter, you will get a screen like this
Notice the blue outline on the first box in the second window. That is the spot you will place a unit of your choice. You can bring in as many units in at the beginning as there are select unit box's.
If you click on one of the units on the to window, this will add them to your select unit window, like so
Now notice the command box in the bottom left corner. See how on mine it has the numbers 0/200. The 0 shows how much command is being used up for that team while the 200 shows how much command you have in total. You do not want the left number to go over the right number as this will add a fatigue penalty making your units move extremely slow. Each unit has a different command cost, so you may want to watch the numbers to make sure you don't exceed your limit. You get a higher command limit when Wil gets promoted at the end of each chapter. Another thing, Wil is the only unit that has no command cost.
Now, see how there are only six unit slots on these screens. You can have a total of nine units in a dungeon at a time after you enter the dungeon, as shown by the three extra unit slots at the bottom of this screen.
To select your other three units, first you need to have at nine units available, which you get more units as the game goes on. Other than that, it's the same way as Kaguya had said to add units.
I hope this will be able to help you in the future.