You can 'roam' with your SIM card from country to country - so even your AT&T card will work in all those countries. That's the good news - the bad news is that you'll encounter prohibitively expensive roaming charges. So it's better to buy a pre-pay card in each country as the previous poster suggested. Certainly in the UK it's a no-hassle process. In some countries (posters have mentioned France) they want a credit card from that country, name, address, telephone number, credit reference.
But the UK is a true capitalistic society - all the vendors care about is your money - cash or credit cards (any nationality) accepted. You simply buy a card and chose either a rolling program that tops up each month or - and more likely to be of use to you - a card which has a certain data volume allowance. Purchase it, put it in your iPad and you're good to go. No set up, no registration, no hassle. When the card's used up - through it away or top up on-line (yes, they all allow you to surf to the company's web site even if your data allowance has all gone, so that you can top up if you want to). It's completely hassle free.
Tim
Scotland