There are quite a few options for picking up a SIM card, kiosks in the airport that will sell you a SIM, kiosks in shopping malls in town, department stores have a department with phones and SIMs, electronic stores sell SIMs, boutique phone stores sell SIMs - some places sell SIMs for a particular company, some have options.
My main advice is don't pay for the SIM without having the sales person help you get it up and running. Once you pay, real customer service can be difficult to obtain.
My next best advice is use WiFi when you can so you don't burn data when you don't need to. Turn data off unless you have a specific need for it. You can always add more data to your card, but why spend more money if you don't need to?
I typically try to stay in one country with a SIM because calls are very inexpensive in the country you purchased the SIM, but roaming when you cross the border. Roaming with a European SIM isn't nearly as bad as roaming with a SIM from the US.
My plan for my next trip (I leave next Thursday) is to try the Orange Holiday plan. I'm in France for 16 nights and the SIM is for 14 days. I'm not sure how much of an inconvenience that will be? The Orange plan may be good for you because it might be good for crossing borders. What I read about it led me to believe it will work in multiple countries but I may not be correct.