How to fix an iPhone 4 that has gotten "sluggish"

Question

1) Make sure it's on and unlocked.
2) Press the Home Key (the "real" button at the bottom of the display twice. That will cause a "ribbon" of application icons to appear at the bottom of your screen.
3) Press any of the icons at the bottom of the screen for a couple seconds until they start to shake and a little '-' shows up in the upper left corner
4) Start tapping the '-' marks. (It's real important that you make sure this is done to the icons that popped up in step 2.) Each time you do the icon will disappear. You are NOT deleting anything from you phone, just removing it from memory
5) Shutdown your phone. You do that by holding both the Home Button (see above) and the Sleep Button (the only other "real" button, located on the top edge of the case until the red arrow pops up. Slide that arrow to the right.
6) Turn your phone back on by pressing the Sleep Button

Answer 1

A clarification of your clarification: If you do what the OP suggested with both buttons the Off slider will appear first and you can let go and slide it over. But the hard reset will do more for the sluggishness.
But the entire suggestion is unnecessary, unless one of the apps in the recently used tool bar happens to be one of the few that actually runs in the background, like Pandora, and you don't want to go to the app itself to stop it, all of this is pointless. The apps aren't running, they've just been recently used.