Force close apps that are causing problems: double tap the Home button to show the multitask bar, then slide the images above the app icons towards the top of the screen.
If Safari is slow, go to Settings - Safari, and tap "Clear History and Website Data".
Restarting might help as well: turn off your iPhone, and turn it on again.
Maybe a reset will improve the iPhone's performance: tap and hold Home and Power button at the same time until the Apple logo appears. Let go of both, your device will power up on it's own.
Disable Background App Refresh in Settings.