Easy answers first. How do we know that Venus does not have ongoing steady plate tectonics like the Earth?

Well, the Earth has a few dozen large astroblemes. Venus has many hundreds. There's no particular reason why Venus should be a bigger target for asteroids or comets than the Earth (and the Moon is ineffective as a shield). So the average age of Venus' surface must be older than the Earth's. 3/4 of the Earth's surface is younger than 280 million years (Ma) (the seabed - you know, plate tectonics...). The other 25% has an average bedrock age of about 0.5-1 billion years (Ga), but the erosional age is about half this. In summary, the average age of Earth's surface at a scale where large astroblemes would show, is about 150-200 Ma. From crater-count ages, we find that Venus averages about 700 Ma - 1 Ga.

Interestingly, no part of Venus is demonstrably older or younger than any other, except where young volcanoes and lava flows have locally resurfaced a small patch, but basically every region of Venus is the same age, more or less.

The radar images of Venus' surface topography can be directly compared to Satellite gravity-derived ocean batymetry and radar altimetry for the Earth. On Earth, plate tectonics is stunningly obvious, if you "drain" the oceans away. You can see the mid-ocean ridges, the transform faults, the subduction zones, the young fold mountains, the matching conjugate continental margins, the volcanic belts, the....

On Venus, there are a few vaguely correlated wrinkles, a couple of patches of highland, and some weak tensional patterns in the lowlands. It looks like plate tectonics tried to have a go, but the crust was too strong.

The standard answer is that ever since Venus boiled off its oceans, the rock dried out and got stronger (traces of H2O act as a wonderful lubricant to hot crustal rocks which "flow" by slow recrystallisation. Without water, crystals stay put and the rock is tougher). In this model, Venus should have frozen its surface about 3 Ga when it got hot and dry. This is not the same as the surface age, and therein lies a secret...*

If you model heat flow on Venus with a thick strong crust, the heat is trapped in the Mantle. it can't conduct out fast enough. Some heat escapes as individual volcanoes and intrusions punch through, but the crust is too thick for that too, and not enough heat gets out. So the Mantle gets hotter and hotter and more and more fluid until finally it has the strength to punch through the crust and tear it open.

At this point, all Hell breaks loose. Literally.

The surface is swallowed into a magma ocean, the planet boils, and finally gets to cool off. But again, the crust reforms and rapidly gets too tough to subduct, once the planet has gone "off the boil". So a new surface forms.

*It isn't really a secret. Plenty people have modelled this and find that a periodicity of 1 Ga +- 50% is about right. So the surface we see today is about the right age for the model, and there were probably 2 or 3 precursors to it, all in the regime of a hot dry greenhouse planet. It's just that most people don't think about climate change and planetary evolution on this sort of timescale and immensity.

Before that, before 3 Ga, Venus was probably very Earth-like, if a bit warm. Plate tectonics, oceans, continents, life, everything.

Then it got too hot...

And the final, difficult answer - "what do I think is respnsible for Earth's tectonic activity?" - Simply the balance of internal heat production, working on an brittle-elastic crust. If you move the Earth in the solar system, or turn the Sun up or down in output, then a subtly or drastically different process would occur. We know that the Sun has warmed through geologic time, but the Earth's surface seems to have stayed relatively constant in temperature (perhaps due to Gaia-style passive bio-geological feedback). So the ultimate answer is that Earth has plate tectonics, because it has life.

That isn't good enough for ever. In another 1 Ga or so, the sun will warm to the point where bio-geological feedback can't stop major greenhouse warming (I mean dozens to 50 degrees here). As the equatorial oceans begin to gently simmer, Life will lose control of the Earth's climatic and geologic stablity, and we will have our own Hell on Earth.