Keep in mind that the Jedi Knights are primarily police. Even the Jedi who devote themselves to the martial school, like Mace Windu, do not generally train in lightsaber combat as rigorously as a Sith does. This is because the overwhelming number of factions that would oppose the Jedi and the Republic are not Force-sensitive and do not wield lightsabers. The Jedi thus train - and fight - against mostly blaster-wielders, and in those cases a single lightsaber to deflect bolts is usually more than adequate, and the focus is on mastering control of a single blade.
The Jedi are also a little more regimented in their training; from Youngling to Padawan to full Knight, most Jedi initiates get the same basic training as any other, and when they progress to Padawan they are counseled by a Jedi who probably grew up in the same system. Only after a Jedi reaches the rank of Master are they learning for themselves and not being taught by another Jedi, and by then their lightsaber training is well-ingrained into the one of the seven single-saber schools.
Now, the Sith came into being as a force opposing the Jedi; they were originally exiles from the Jedi Order, and created the Sith Order with the specific goal of taking their revenge on the Jedi. As a result of both that, and the nature of the Sith themselves to fight each other for dominance, Sith expect other Force-sensitives as opponents. So, they train very rigorously in lightsaber combat, especially saber-vs-saber styles like the very antiquated Form II, and adopt novel styles of combat (such as lightwhips, ergonomic "fencing" sabers like Dooku's, staff-styles like Maul's, and yes, double-saber styles) that are unfamiliar to even experienced Jedi. As a result, Sith more often than not mop the floor with the average Jedi Knight.
Also remember that the Dark Side can make one very powerful, very quickly. It can take decades to become a Jedi Master. Count Dooku was already a very experienced Jedi Knight before falling to the Dark Side, and as such it took one of the most experienced Jedi - Yoda - to stand a chance against him, and even then the fight was a stalemate. It took an even more powerful (and emotionally unhinged) Jedi - Anakin - to finally defeat him, and it's also thought that Palpatine told Dooku to hold back against Anakin.
Case in point: when Obi-Wan tossed Anakin a second lightsaber in Ep. II, Anakin was able to draw on the Force to be effective in dual-saber style, but he was obviously inexperienced in that style; according to EU sources, Anakin practiced Form V, which is very strength-dependent, and is more suited to two hands on one saber for leverage. His unfamiliarity with dual sabers, and with Form III or IV which would have been better suited to using two sabers, resulted in a mistake that lost him one of the sabers. So, he reverted to his natural single-saber Form V style, which lasted longer as he was more comfortable and experienced in that style. He still lost to Dooku, who first had a few decades' experience as a Jedi over both Obi-Wan and Anakin, and second had trained even more purposefully under Palpatine to fight Jedi using Form II, which is antiquated but highly effective against a lightsaber-wielding opponent.
We never saw anyone use more than one lightsaber in the original trilogy. Of course, the only three lightsaber-users in that trilogy were Obi-Wan, Luke and Vader, so it's a relatively small pool, but the initial stage direction Lucas gave all the lightsaber-wielders was a very heavy Kendo style, as if the lightsaber blade were as heavy as a nodachi or broadsword. The development of alternate weapons and fighting styles was originally developed in the EU through fan involvement, including the background behind the physics of a lightsaber like the fact that the blade is near-weightless but subject to other forces. Elements of the EU then bled back into G-canon in the prequel trilogy as Lucas and the scriptwriters looked for ways to kick the fighting up a notch from the original trilogy. The first change was to the pace of fighting; the choreography drastically increased in tempo. The second was the inclusion of alternate fighting styles and variations of weapons. We never did see a lightwhip, but dual-saber and staff styles made it from the comics and novels to the movies.