One way to fix this is to select the object, for example, the arm, and then select the armature. Be sure you take the armature into edit mode and select only the bones you want to have effect on the arm.
Once this is completed, parent the object to the selected bones using Ctrl+P > With automatic weights.
Do this same thing for the rest of the model.
Edit 2: Here is a step-by-step for applying an armature to separate objects.
Step 1: Select the piece you want to be the child of the armature by right clicking on it.
Step 2: Select the armature, also by holding Shift and right clicking on it.
Step 3: In the bottom left of the 3D viewport, switch to pose mode.
Step 4: right click on the bone(s) you want to be the parent of your object.
Step 5: Press Ctr + P, then select "with automatic weights.
that bone is now applied to the object, repeat this method for the rest of the model.