How do we know that the Universe is still expanding now? Yes, I know that most galaxies have a red shift and that means they are moving away from us. 

The problem is that the farthest galaxies are 13.8 billion light years away. That means that the info is 13.8 billion years old.

What has been puzzling me for years is that the red shift observation shows that the galaxies were receding 13.8 billion years ago. We don't have direct data on what they are doing now. It is natural that the universe was expanding with a tremendous speed at that time because it was near to the big bang, but how do we know that it still is?

If the furthest galaxies are moving with higher speed than the nearer, that means to me that their speed is reducing with the time.
You're right that in principle we cannot know if the distant galaxies are still receding from us. When, however, we think that they indeed are, it hinges on the cosmological principle, viz. that the Universe is homogeneous and isotropic, i.e. "looks the same everywhere and in all directions". This is a philosophically motivated statement, which is continuously tested observationally. So far, there has been no significant experimental evidence that this is not correct.

When we observe the velocities of galaxies throughout the Universe, we see a smooth velocity as a function of time, or distance, with some intrinsic scatter which is due to the gaalxies' peculiar motion, i.e. their velocities through space, which is usually of the order of 100–1000 km/s. That is, distant galaxies move away from us fast, and nearby galaxies move away from us slowly. As you say, the expansion rate decreased with time, but only until a certain point, after which it started increasing again (due to dark energy).

The fact that we see that nearby galaxies are still receding, together with the cosmological principle, implies that the distant galaxies should also still be receding. We know of no reason that they shouldn't. Of course this is no proof, but in physics, there are no proofs, only verifications and falsifications. To postulate that the distant galaxies no longer recede, and to be taken seriously, you would need to come up with an experiment that could verify this hypothesis, preferably along with a mechanism that would be able to cause this phenomenon (this looks a bit condescending when I type it; this is not my intention).

The expansion rate is currently — and hence locally — around $70\,\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$. Due to the aforementioned velocity scatter, we cannot probe expansion below ~1 Mpc, but at this scale, space doesn't really expand anyway due to the mutual gravitational attraction of the Local Group. This means that in principle, the expansion of the Universe could have come to a halt within the last few million years, and still be in accord with the cosmological priciple. However, this would mean that the evolution of expansion velocity as a function of time would have a sharp kink. Again, this is not impossible, but we know of no physical mechanism which would be able to cause this.