How we know
Four motions stack on top of each other, and none of them ever switch off. The Earth's equatorial circumference is 40,075 km and it turns once every 23.93 hours, so at the equator the ground carries you east at roughly 1,670 km/h. That is the figure NASA's Earth Fact Sheet lists, usually rounded to over 1,600 km/h.
The whole spinning planet is also falling around the sun. NASA puts Earth's mean orbital velocity at 29.78 km/s, which works out to about 107,000 km/h. The sun in turn drags the entire solar system around the centre of the Milky Way at roughly 230 to 240 km/s, over 800,000 km/h, a speed measured by VLBI maser parallaxes in Reid et al. 2014.
The biggest number is measured against the cosmic microwave background, the leftover light of the Big Bang and the closest thing physics has to an absolute frame of rest. The COBE satellite (Kogut et al. 1993) and later Planck (2018) found the solar system moving at about 370 km/s and our Local Group of galaxies at roughly 620 to 630 km/s against that backdrop. That is more than 2 million km/h.
What it means
You feel none of it, and that is the genuinely strange part. Your inner ear and your body only register changes in motion, acceleration, not motion itself. Steady velocity exerts no force you can sense, the same reason a smooth plane at cruising altitude feels like a still room.
Everything around you moves with you at the same speed, including the air, the chair, and the coffee in the cup, so there is nothing to push against and nothing to feel. Stillness is a sensation, not a fact. By every physical measure you have been moving since before you were born.
The honest caveat
There is no single true speed, because there is no universal "stationary" point to measure against. Each number is a speed relative to something specific: the ground, the sun, the galactic centre, or the cosmic microwave background. The over-2-million-km/h figure is the most absolute one available, your motion relative to the early universe itself. Add the four together and you have never, in any frame that matters, been still.