In The Phantom Menace, Palpatine begins his ploy to gain control of the galaxy is as follows:
Step 1: Under the guise of Darth Sidious, he manipulates Viceroy Nute Gunray into creating a trade boycott on the planet Naboo.
Step 2: After some time, Palpatine/Sidious orders Viceroy to begin invading Naboo. In order to make the invasion legal, Gunray needed to force Queen Amidala to sign a treaty, however the Jedi had helped her escape the planet.
Step 3: When Queen Amidala arrives on Coruscant, Palpatine convinces her that Chancellor Valorum is powerless against the bureaucrats, who are on the Trade Federation's payroll, and to start a vote of no confidence in the Senate against Valorum.
Step 4: After the vote of no confidence passes, Palpatine informs Queen Amidala that he was among the three chosen replacements as Chancellor. Instigating the invasion of Naboo was to help generate sympathy in the Senate to garner his nomination and election as Chancellor.
Step 5: Queen Amidala insists on heading back to Naboo, Palpatine pleads for her to stay, presumably hoping that the conflict will escalate and create a schism within the Senate itself. However, she refuses to abandon her people. So as Darth Sidious, he informs Nute Gunray to wipe out all the resistance and to capture the Queen.
Step 6: After the Trade Federation unexpectedly loses the battle, Nute Gunray and his staff are sent to stand trial in the Senate. With the power of the Trade Federation temporarily broken, the balance of power within the Galaxy has been restored for the moment. This is a setback for Palpatine, now Chancellor: with his assistant Darth Maul dead as well, the political instability he was hoping to exploit is averted, and he needs to bide his time for when another opportunity arises. However, he befriends Anakin, seeing potential in him as a future assistant in his scheme.
For the next steps, see Star Wars: Episode II - Attack of the Clones