How do I properly bring in coax from the pole to the interior of my house?
Cable companies should not be penetrating the building with cables like the way you describe.  Water can flow down this wire and into the building if it's not sealed properly.  And if it is sealed properly, if the wire is able to be moved in and out because it's not securely anchored then it will eventually be able to leak should water get around it.  

Have they also put a bend in the wire below the entry point to prevent water flowing into the house?  Have they anchored the wire so it can't move in and out ?

Several easy ways I've found to put wire into the building without drilling unsightly holes and that won't cause leaks.

1) Go under a flashing.  On my house we have an old iron roof with lead flashing.  I've been able to put a wire up under the flashing.  I just lifted the edge of it slightly and pushed it in. Then I bent the lead flashing back down over the wire.  As the antenna was downhill of the flashing, water couldn't go up the wire in any way and enter the house.

2) Bring the wire down to the guttering, and poke the wire up under the edge of the roof.  Usually there is a gap to allow ventilation.  This allows you to get the wire into the attic space and you'll then be able to put it into any room you desire.

3) Bring the wire down one of the downpipes.  Then if you happen to have a raised foundation like my house, put it through one of the ventilation ducts at ground level.  I then bring it up into a wall cavity from below. 

4) You could also bring the wire in through a hole in the sofit and then into the ceiling space where you could then bring it down into the house through an internal wall.  Not as tidy or as easy as just ducking in under the iron though.

Important: Water can flow down a bent wire through surface tension.  So wherever it enters, make sure it can't do that by putting a sharp bend in the wire just below the entry point.  That way any water will run off on the outside and not into your home!



Update: I see that they have anchored it and added the loop at the bottom. And there does appear to be some sealant around the entry point.  It should be OK, but it is really ugly and doesn't pass any tests for beauty.



Update2: Since you want to enter from below this is what I suggest.
Re-route the cable down the down pipe that I see running down the wall.
Clip the cable to it using appropriate UV rated cable ties.
It appears to me that your house is raised on some concrete or wood piles. It looks similar in construction to my house where there is a concrete foundation around the outside of the house and probably concrete or wooden piles within.  If that's the case then if there are vents in this (there really should be) you can poke your wire through one.  If not, drill a hole through that outer foundation.  It'll require a long bit and a powerful hammer drill  - take your time.  Then once you are through, poke your cable through and you can then bring it into whichever room you wish.