Website sizes

When you are designing a responsive website how do you go about deciding the sizes in pixels each layout would be? how do you know how big to make the website?

You don’t have to decide this if you don’t want to. You can just let the content expand and contract as needed. You just might want to set a max-width so that things don’t expand too much. Depending on your design, you may find that, as some points, it’s best to step in and set something to width: 100% rather than floating it (for example) … but that’s different for each design.

As far as I know, the most common used page widths in responsive design are 960 or 1000px for desktops/laptops, 768 or 800px for small tablets, and 320px (or 240px for really small ones) for smartphones.

As you very correctly said, these days desktops are very common with the resolution 1024 * 768, so one can prefer using 980 - 1000 px as the width.

Fixed width design is really past its sell by date because you can expect your visitors to use anything from 300 px wide to 2000px.
If your width is smaller than the visitiors scree, it looks ridiculous with large blank spaces on eithe side.
If it your screen is wider, you need to use the horizontal scroll bar to read the text, which is annoying enought to send most visitors packing. As mobile device use is growing faster than anything else, you lose out on the fastest growing market with fixed width design.

Maybe. You can set the page to fill the user’s screen easily enough, and some devices let you double tap to zoom in … so it may not be so bad. (I still don’t recommend fixed width, mind you, but it’s ot the end of the world.)

No, it certainly isn’t the end of the world, and clever phone users will know how to patch it.
But… a lot of phone users are NOT clever, don’t know how to patch it and will just be irritated. Irritated users are less likely to stay and less likely to buy. Visitors are getting more and more used to ease of use, and silly, outdated problems like fixed width design give a really bad image to a company that still uses this antique way of desing imho.
Maybe I’m just a difficult customer, but when I try out a shop and there is a queue of people waiting to be served, I’m out. If I visit a website that loads slowly or is hard to navigate, I’m gone. If dealing with the company is pita before they got my money, I really don’t want to know how they are after they got my money, and I have a problem with their product.

I’m sure anyone using a smart phone will at least know how to zoom. But yes, there’s a lot to be irritated by, nevertheless.

when I try out a shop and there is a queue of people waiting to be served, I’m out. If I visit a website that loads slowly or is hard to navigate, I’m gone…

Unless you find you’ve got to have the product, no matter what … which a lot of companies seem to rely on.

I don’t quite know the situation in Oz and to what the degree the recession is hitting, but in the UK and Europe it has hit hard with no signs of abating.
5 years ago, it was a sellers’ market for almost anything, which has done a 180 and now it is a buyers’ market for all but a few items. I expect the vast majority of companies that still believe the consumer depends on their product or finds it absolutely necessary to have it (like Apple), will soon wake up to a very painful reality.
This day and age, you have to stand out from the rest and be the best you can be (hate that cliche), and having yesteryear’s webdesign doens’t help to do that.