You'll need to know the frequencies and protocols used by your carrier and ensure they are supported on your iPad. 3G is highly likely to be OK but it's not 100% (for exampled, much of T-Mobile's 3G network runs on a frequency that's not compatible with the current iPad/iPhone
As noted, you'll need to cut the card down to nano-SIM size. If you screw it up, the SIM is toast and will need to be replaced. You'll also need an adapter if you want to put it back into the phone.
The iPad needs to be configured with the proper data/APN settings for your carrier.
Your carrier has to not care that you are doing it. I've heard stories about carriers detecting that a phone SIM is being used in a tablet and disabling the SIM.