[Fluid_thinker (OP)]

Particles obtain energy from their environment. But how do they actually move? they dont have an inbuilt propulsion system, so how come they dont just store the energy or heat up and remain where they are?

[imatfaal]

Conservation of momentum/conservation of energy - particles bump into each other, or get a bash from a photon and that motion (which could be averaged out as heat) is maintained.  Particles don't just possess energy (other than through their mass and strong nuclear / electro magnetic forces for compound particles) - they vibrate or move, and they move cos they were crashed into by another particle

[evan_au]

so how come they don't just store the energy...and remain where they are?

Sometimes they do - a molecule of explosive stores chemical potential energy, and stays (fairly) still for most of its existence.

So how come they dont just ... heat up and remain where they are?

What we feel as heat is actually the kinetic energy of particles, bumping into the atoms of our skin.
The thing that normally keeps them in (roughly) the same place is that they don't travel very far before they bounce off another particle.
If these particles were given the same energy in a vacuum, they would go flying off at pretty much the speed of sound (or even faster if they were hotter, like from an explosion).

how do they actually move?

Because the particle experienced a force, and that caused it to be accelerated: F=ma (Force=Mass x Acceleration, according to Newton).
For every force, something else experiences an equal and opposite force, also according to Newton, so it starts moving in the opposite direction.
A molecule of explosive releases the chemical potential energy as motion of the atoms and molecules flying apart at high speed. We feel this motion as the heat of the explosion.

[Fluid_thinker (OP)]

Understand the replies concerning conservation of momentum from collisions and F=ma.

Assuming I was to take Hydrogen atoms and cool them to close too or if possible, absolute zero in a vacuum.

Does the vibration stop? Do the Electrons still occupy the same space? Or do the Electrons too lose energy and hence the space compresses/shrinks? Ultimately, I assume the atoms is now stationary.

If I tend allow the atoms still in the vacuum to rise above the absolute (or near absolute) zero, what happens?

Does the Electron re-occupy 'its' space? Does this introduce movement of the atom? Does the atom start vibrating again to the point that the Hydrogen atom will start to obtain momentum and if the temp rises significantly this becomes the fast moving atom.

I am assuming no other particles other than Hydrogen are involved.

[yor_on]

According to HUP you have a uncertainty of position, depending on way of observing, that can be read as there are no 'still' particles ever.

[Phractality]

The mainstream answer is that particles with mass can't change velocity without an input of momentum; inertia is just a property of matter. That amounts of a truism. For a more in-depth answer, you have to look outside the mainstream. I personally believe particles are collections of waves which can only move at the speed of light. That's all I can say on the mainstream board. Try asking on the New Theories board.