Ok, let´s try this step by step.
1. Your sensors are active (already done) and the enemy ships are in range (they show on the map with a size:
"Boulder 001, TH 800, 6583 km/s, 6500t"
if there is no size (6500t), you don´t have them on active, only on passive.
2. They are in range for your firecons (only applies for missile firecon) and they show up on the "Assign contact as target" window, (Battle Control window (F8), lower left)
3. On that window: Select Firecontrol (uper left), select target (lower left), hit "Assign".
This firecon will now try to shoot at this target.
4. Assign Weapons to the selected firecon (middle left). If weapons are missile launchers, assign missiles to the launchers (center)
5. Repeat for other ships _or_ hit the Copy Target: "Class in TG" button (center right), if you want all ships of that class in the taskgroup to fire at the same target
6. Once you are done for all ships, hit the Current Fleet: "Open Fire" button (red one, lower right)
Your fleet should now start to shoot, or, if something is amiss, at least give you some messages about _why_ it is not shooting.