With your iPad connected to iTunes, select the iPad under devices. Go to the Apps tab and make sure sync apps is turned on, including the auto sync at the bottom. Now, if you normally sync with iTunes, do so now and all the apps should be loaded into iTunes.
If you don't want to do a full sync, right click on the iPad under devices and choose Transfer Purchases. That should also move all your apps to iTunes.
When you connect your iPhone, you'll want to visit the same area and select the apps you want. You have to be set to sync and each app you want to sync must have a checkmark next to it.
Some apps are iPad only. If they are not compatible with the iPhone they will not show up in the list of apps available to sync when the iPhone is connected. Some developers make their apps universal, and some write separate apps for each device. Often the names are so close that it isn not immediately obvious which is which.
The sure fire way to know is to look at the app in the App Store. If there is a plus sign in the price/free button then it should work on both devices. If not you'll have to buy the iPhone version if you want the app on that device.
Somewhat familiar with this, since I just spent the last three hours setting up and playing with my new iPhone.