Good question.

You ask:

How did just one (or 2 if you count trainees) Sith Lord - even as powerful as Sidious - diminish all of Jedi's ability to use the Force, seemingly everywhere in the Galaxy?

The answer is that he can't. :)

In fact he didn't literally changed the force abilities of the Jedis. He changed the Force itself. Look at this passage in The revenge of Sith:

And while Palpatine answered, Mace Windu reached into the Force. To Mace's Force perception, the world crystallized around them, becoming a gem of reality shot through with flaws and fault lines of possibility. This was Mace's particular gift: to see how people and situations fit together in the Force, to find the shear planes that can cause them to break in useful ways, and to intuit what sort of strike would best make the cut. Though he could not consistently determine the significance of the structures he perceived—the darkening cloud upon the Force that had risen with the rebirth of the Sith made that harder and harder with each passing day—the presence of shatterpoints was always clear.

From Labyrinth of evil

Yoda surrendered himself to the current of the Force. Sometimes, when the current was swift and steadfast, he could see through the eyes of his fellow Jedi, almost as if they were the Temple's remote sensors. And sometimes when the current was especially forceful, when it surged as if descending from great heights, he could hear the voice of Qui-Gon Jinn, as clearly as if he were still alive. Master Yoda, he might say, we still have much to learn. The Force remains a code only partially deciphered. But another key has been found. We will become stronger than we have ever been... Today was not one of those days. Today the current was interrupted by eddies and whirlpools, hydraulic traps whose roar overpowered the voices Yoda sought to hear. Today the current was not pellucid, but muddied by red soil eroded from distant shores, treacherous with obstacles, tainted. Though he was scarcely aware of it, his eyelids were squeezed tight, his eyeballs dancing beneath as if incapable of focusing on any one thing. He had an image of himself drawing aside a veil only to find another, and another beyond that. The dark side frustrated his every effort to see clearly. The experience was still something new to him. Even though he'd had centuries to grow accustomed to foreboding, he had lived far longer without it. The dark side never completely disappeared - - it scratched at the surface like an insect crawling across a transparisteel panel - - and he had been able to sense its incremental increases in strength when the Jedi erred, or when the Republic erred, and soon the two were hand in hand.

The Jedi are the servants of the light side the force. The weaker it gets, the harder it is to see clearly, as the dark side does everything it can to deceive them.

The Sith made the Dark side stonger.

They used three methods to do so:

Force technics:

The Force is influenced by all living being, that's why all places don't fell the same in the Force. If a place is inhabited by beings full of fear, anger and hatred, the place will become strong in the dark side (Korriban). For a being strong in the Force, a single time can be enough: the place where Anakin's mom died remained tainted for at least decades. From the study of the Force, it's possible to do it consciously, both Jedi(Shaak Ti on Felucia) and Sith did it.

Plagueis and Sidious did the same for the entire galaxy(Darth Plagueis):

The question of whether he and Sidious had discovered something new or rediscovered something ancient was beside the point. All that mattered was that, almost a decade earlier, they had succeeded in willing the Force to shift and tip irrevocably to the dark side. Not a mere paradigm shift, but a tangible alteration that could be felt by anyone strong in the Force, and whether or not trained in the Sith or Jedi arts. The shift had been the outcome of months of intense meditation, during which Plagueis and Sidious had sought to challenge the Force for sovereignty and suffuse the galaxy with the power of the dark side. Brazen and shameless, and at their own mortal peril, they had waged etheric war, anticipating that their own midi-chlorians, the Force’s proxy army, might marshal to boil their blood or stop the beating of their hearts. Risen out of themselves, discorporate and as a single entity, they had brought the power of their will to bear, asserting their sovereignty over the Force. No counterforce had risen against them. In what amounted to a state of rapture they knew that the Force had yielded, as if some deity had been tipped from its throne. On the fulcrum they had fashioned, the light side had dipped and the dark side had ascended.

The spread of chaos

So we've see, beings can corrupt the Force. In the first case, a few but immensely powerful beings can make a galactic change. The other way round, weak but extremely numerous individuals can do the same. So the Sith had to spread misery to create fear, anger and hatred.

“Through us, the powers of chaos are harnessed and exploited. Dark times don’t simply emerge, Sidious. Enlightened beings, guiding intelligences manipulate events to bring about a storm that will deliver power into the hands of an elite group willing to make the hard choices the Republic fears to make. Beings may elect their leaders, but the Force has elected us.” He glanced at his apprentice. “Remember, though, that a cunning politician is capable of wreaking more havoc than two Sith Lords armed with vibroblades, lightsabers, or force pikes. That is what you must become, with me advising you from the dark.”

Since the refondation of the order by Bane, the Sith have been fomenting revolts, encouraging slavery, making the political institutions dysfunctional, increasing social tensions, and so on, culminating with the Clone Wars. This gave strength to the Dark Side.

The Fall of the Jedi

From the Revenge of the Sith:

Mace looked even grimmer than usual. "Since the fall of Darth Bane more than a millennium ago, there have been hundreds of thousands of Jedi-hundreds of thousands of Jedi feeding the light with each work of their hands, with each breath, with every beat of their hearts, bringing justice, building civil society, radiating peace, acting out of selfless love for all living things-and in all these thousand years, there have been only two Sith at any time. Only two. Jedi create light, but the Sith do not create darkness. They merely use the darkness that is always there. That has always been there. Greed and jealousy, aggression and lust and fear-these are all natural to sentient beings. The legacy of the jungle. Our inheritance from the dark."

This quote is filled with Jedi propaganda IMHO, but there still is a valid point. The Jedi made the light side far stronger just by existing, and made active efforts to make it even stronger. The Clone Wars was the solution. Many great Jedi fell because of the war (Dooku, Deepa, Vos), and even those who did not strayed where tainted:

From Labyrinth of Evil