It is, and should be, very simple to make.
The first thing you need is a good frying pan - nothing too flimsy, or too heavy for that matter.
Then you need lots of floury mashed potatoes. They can have been mashed with a small amount of warm milk, and or some butter, and a pinch of salt if it is not going to be given to a baby, or a young child. You shouldn't use much butter or milk as we are not aiming for smooth mashed potatoes. Slightly chunky is actually much better, as long as the potato is cooked through. Please don't use roasted or new potatoes, the texture is not at all suitable for bubble & squeak. Also, please don't add any other leftovers eg. parsnips, carrots, peas etc. They actually detract from the flavour of the Bubble&Squeak!
Next, chop in half about two thirds of pre-cooked, al dente, sprouts, and roughly mix them with the potatoes. At the same time, heat about a tablespoon of butter, and a little cooking oil in the frying pan. Then, when the fat is all melted and quite hot, add the first portion of the potato and sprouts into the pan. As others have said, the bottom of the mixed b&s should go quite brown and crispy, and when that happens, use a fish slice to turn the mix over in chunks - you may/will probably need to add some more melted butter, and a little heated oil (melting and heating in a microwave for a few seconds is probably the easiest way to do that) to the pan, to keep the mix slightly moist, and make the new bottom of the mix crispy. If you have quite a few guests to feed, or you have a very big appetite (I have when it comes to b&s!), or only a small frying pan, keep your already fried b&s hot, while heating up and crisping the next batch of b&s.
*The already prepared and heated mixture should have any extra, visible, liquid cooked off it quickly, before removing it from the pan.
When serving, have salt and white pepper available for any adult who might want to add a little extra spice, to their meal. In our house, this annually eagerly anticipated meal is also served with pickles, red cabbage, and cranberry sauce available. It is also great served with many fifferent cold cuts of meat