How did Sidious get his lightsaber back after losing it in his battle with Mace Windu and before his fight with Yoda?
Sidious actually had at least two identical or near-identical lightsabers, which he kept concealed in his office on Coruscant during the Clone Wars era. One in particular, the example he used during the confrontation with Master Windu et al, was kept inside of a statue on his desk and was lost during the confrontation. The one he used in his duel with Master Yoda was a different one that followed the same design.
For the most part, it would seem (according to what we see onscreen) that Sidious preferred to only use one lightsaber at a given time. However, in Star Wars: The Clone Wars S5E16 "The Lawless", Sidious is shown using two lightsabers at once on Mandalore: