How do the blades on a propeller generate thrust?
The picture of the turboprop is probably confusing you because you are looking at a shutdown engine.  For a multi-engine propeller airplane a desirable feature is that the propeller with auto-feather when shutdown, so that an in-flight engine failure will cause the prop to be in a minimal drag configuration.  This minimal lift, minimal drag configuration is what you posted, and this is not producing thrust.  When the engine is started and system pressure (oil, hydraulic, whatever controls the adjustable pitch prop for that particular engine) will drive the propellor pitch angle into lift-producing regimes.  Turboprops also typically feature "Beta" propellor pitch, which allows the propellor pitch to be adjustable past zero-lift into negative-lift and is used for landing rollout and (in some airplanes, perhaps not many) slowing down in-flight or steep descents.  During normal flight the turboprop propellor is producing lift just like the propeller on the cessna you are familiar with.

The N1 fan in a turbofan (the big one you see when you look at the front of the engine) is a ducted fan.  The individual blades of the N1 fan are angled to push air backwards.  This works the same way as a big box fan you can buy at walmart.  The key difference is the N1 fan rotates an order of magnitude faster than a box fan.  The bypass air is accelerated by this fan and exits through the rear of the engine to produce thrust.