Visually inspect the "reveal" around exterior doors. Look for light coming through. If light gets through, air will too.
For large gaps you might need to use backer rod to fill the space. Measure the gap from side to side and cut a piece of backer rod to fit. Add a bead of caulk to one side of the cut piece and push it into the gap. Push it as far into the gap as possible, then push it into the space as far as it will go. Larger gaps might require more than one piece.
Once the space is filled, caulk both the upper edge and the lower edge, and don't worry about getting a perfect bead. No one will see your handiwork -- the goal is just to seal off any air penetration. Stick the decorative trim against the caulked area then drive in some finishing nails to secure it.
Check weather stripping around the exterior doors. If you need to replace old or damaged weather stripping, first you need to remove the old weather stripping. Determine the style of weather stripping you need and follow the manufacturer's instructions for installation.
Starting at the bottom, slowly move your way up the door frame; make sure the foam sticks evenly into the corner created by the door frame and the door stop. You can use a putty knife or a 5-in-1 tool to help wedge the foam strip firmly into the corner seam. Once you have reached the top, cut off the excess and press the end firmly into the corner. Then remove the tape covering.