How do I know which applications slows down the phone, so that I could get rid of them?
Although you can't find out what apps are 'slowing down' your phone, you can find out which apps are using your battery the most. Generally if apps are using a lot of battery power, they're probably slowing down your phone too.
You can find the list of apps vs battery usage in Settings > Battery.
The Watchdog Task Manager app is really great for these kinds of problems.
There is yet another aspect, Constantly running background (daemon) services that are usually associated with network updates, mails, facebook, sugarsync, dropbox etc.. can get the juice out of your phone very quickly, you need to keep track of such 'zombie' apps that keep these background services running. Look at them once and make sure you keep what you need. Be careful it can have lot of side effects.
Settings -> applications -> manage applications -> running (tab)
Hope it helps you.
I've published an app called Wakelock detector on Google Play which may help you.
In Android, wakelocks can be used by apps to keep your phone running even when you turn off the screen. My app shows currently running apps with their wakelock information.