Get your vegetables chopped first. I would use, for a basic vegetable soup, one onion - peel it and halve it, then cut each half into small dice/pieces (get rid of the woody root bit if you like). Put to one side. A couple of carrots - peel them and cut off the ends, wash under the tap. Again, chop into dice (think dolly mixture) and put to one side. A couple of celery sticks or a leek; chop the ends off, wash (especially the leek which can trap dirt in between its layers). Dice.
Get a big saucepan. Put on hob, heat 2 tablespoons of olive oil or vegetable oil on a medium heat. Wait a minute or so for it to warm then put in the diced onion. Move it about with a wooden spoon to coat it in the oil. After a while it will start to look a bit see-through. If the heat is too high it might burn/go golden - you don't want this, so turn the heat down. Once the onion is softening, put in the carrot dice and the leek/celery dice. Stir around in the oil, let them soften (keep the heat medium/low so they don't burn).
After 5 or so minutes your veg are soft and there will be a base of flavour. You can add different things, perhaps a tin beans (cannellini, borlott, rinse them in a sieve under the tap first so you don't include the canning liquid). A tin of chopped tomatoes. Stir it all together.
Then you need a bit of hot liquid so stick the kettle on. You can use a stock cube or that stock powder made by Marigold in little tubs (a couple of teaspoons dissolved in boiling water). Presuming you don't want to make bucket loads, put about 1 litre (use a measuring jug) or 1.5 litres of boiling water and dissolved stock cube/powder into your saucepan. For extra points, swirl some of it round the empty tin of tomatoes and empty that in for more flavour.
Season - i.e salt and pepper. I like a good teaspoons worth of salt and some black pepper but other people will think that's too much.
Bring the saucepan of stock and veg to the boil - wait until little bubbles appear around the outer edge and then slowly spread so the whole pan is boiling. At this point turn it down low so you have a gentle occasional boil. Let it cook for about half an hour.
This is your soup. If you want it taste better, let it cool, put it in a Tupperware in the fridge and reheat the next day, it will taste much better. But you can of course eat it now, maybe grate some parmesan on top.
Nigella is great on vegetable soups, so is Nigel Slater. Don't be scared. The peeling and chopping is the time consuming part. Some people buy a bag of ready-chopped vegetables to speed things up but my mother told me I would go to hell if I did this so I can't.