How to Grocery Shop in Europe
I should start by saying I haven't gone grocery shopping in every EU country, but have done so in many of them. I believe the UK isn't so dissimilar to the US, but many of the other countries are. You could figure out how it all works easily enough, but if you've just relocated to country in which you don't speak the language, it's always best to have some bit of a clue before you do something. Even something as commonplace as grocery shopping, particularly when it can be such a different experience to where you've spent most of your life. The following tips will help you transition more smoothly and fit in more with the locals, which is what you really ought to be doing when you move abroad. These things may not apply to all countries, but has been my experience in Holland, Belgium, Germany, Austria, Switzerland, Denmark and a few others.
When you see the signs for these in English (if you see any signs in English at all, that is) these are called trolleys in most parts of Europe because that's what the British call them. If you're traveling by car and parking in a lot, there will likely be a return area for shopping carts, and you can get one from there before you enter the supermarket. Otherwise, you can get one at the entrance -- sometimes they will be inside and sometimes outside. Regardless, you will most likely need a coin to get the cart in the first place. This is incentive to get people to return the carts to their proper location: you get your coin back when you link your cart up to the one in front of it. It's pretty clever, really, and certainly works better than the US system.
In many countries these can be hard to find. Sometimes they are well stocked, but I can tell you that where I live the staff are slow to collect them and take them back to the front entrance, so people have to go to the checkout lines first and get one from the stack there. This isn't always the case, just something to be aware of.
Fruit and vegetables
Some shops will not require you to weigh and put a sticker on your fruits and vegetables. You'll be able to tell which is which, because they will have a scale (just so you can check the weight) but no stickers. Some shops will have a little counter where a shop assistant will do this for you, you put your stuff on their scale and they print the sticker and put it on your bag. And some places will have it set up so that you do it all yourself.
Waiting in line
In many countries there are long lines at checkout, but people tend to buy food daily or every few days so they don't have too much to buy. In some countries there aren't many dividers for the conveyor belt and you will need to watch your stuff closely to make sure it doesn't end up getting rung up with the person in front of you -- and that you don't get stuff the guy behind you wants. Also note that many places have very short conveyor belts and you will have to wait and load your stuff up every few seconds if you've got a lot of stuff. (Another reason to not buy in bulk.)
You can pay with debit cards and the like in the EU. If you pay with cash they will almost always want you to pay with the coinage amount as well. You can pay with larger bills, obviously, but if you've got the 45 cents, they will want that as well. And they will often look annoyed when you haven't got it. Mind, don't use super large bills as if they can't make change they will just shrug and tell you can't buy anything.
This is not the USA, there are not teenage baggers standing at the end of the conveyor belt, ready to pack your stuff up. Well, not anywhere I've ever shopped, anyway. 99.9% of the time you will have to bag your own stuff and if you want plastic bags (they rarely have paper bags here because most people bring their own reusable bags) you will have to buy them from the clerk. Keep this in mind before you go loading up the conveyor with lots of stuff, cos they won't wait for you to pack it all up before they start ringing the next customer up (again, not where I live, anyway). If you really need to buy in bulk they easy way to do it is fill your cart back up after they are rung up and then pack the bags after you've paid and left the line. There are usually tables set up around the checkout area for precisely this reason and it makes everything so much easier.